Etymology
The English word “baptism” is a loanword derived from the Greek words βάπτισμα and βαπτισμός.1 Both of these Greek nouns are related to the Greek verb βαπτίζω, from which is derived the English verb “baptize,” also a loanword.
In A Comprehensive Etymological Dictionary of the English Language, Ernest Klein wrote,2

The Hebrew Verb טָבַל and Noun טְבִילָה
The Hebrew equivalent of the English noun “baptism” and the Greek noun βαπτισμός is the noun טְבִילָה (tevila), which is related to the verb טָבַל (taval), essentially meaning “to dip.”
Heinrich Friedrich Wilhelm Gesenius wrote,3

While the noun טְבִילָה does not occur in the Hebrew Tanakh, it does occur often in the Mishna and Gemara (a.k.a. Talmud) and contemporary Jewish literature.
Regarding the noun טְבִילָה, Marcus Jastrow wrote,4

The Hebrew verb טָבַל occurs 16 times in 16 verses in the Hebrew Tanakh. It is translated in the 1769 ed. of the King James Version as follows: dip (15x), plunge (1x).
The following table lists the translation in the LXX of each occurrence of the Hebrew verb טָבַל in the Masoretic text:
Verse
Hebrew Text
Greek Text
Gen. 37:31
וַיִּטְבְּלוּ
ἐμόλυναν
Exo. 12:22
וּטְבַלְתֶּם
βάψαντες
Lev. 4:6
וְטָבַל
βάψει
Lev. 4:17
וְטָבַל
βάψει
Lev. 9:9
וַיִּטְבֹּל
ἔβαψεν
Lev. 14:6
וְטָבַל
βάψει
Lev. 14:16
וְטָבַל
βάψει
Lev. 14:51
וְטָבַל
βάψει
Num. 19:18
וְטָבַל
βάψει
Deu. 33:24
וְטֹבֵל
βάψει
Jos. 3:15
נִטְבְּלוּ
ἐβάφησαν
Ruth 2:14
וְטָבַלְתְּ
βάψεις
1 Sam. 14:27
וַיִּטְבֹּל
ἔβαψεν
2 Kings 5:14
וַיִּטְבֹּל
ἐβαπτίσατο
2 Kings 8:15
וַיִּטְבֹּל
ἔβαψεν
Job 9:31
תִּטְבְּלֵנִי
ἔβαψας
The Hebrew verb טָבַל and its conjugations are consistently translated by a conjugation of the Greek verb βάπτω in 14 of its 16 occurrences, or approximately in 88% of its occurrences. It is translated by a conjugation of the Greek verb βαπτίζω once, in 2 Kings 5:14, and by a conjugation of the Greek verb μολύνω also once, in Gen. 37:31.
The Greek Verbs βάπτω and βαπτίζω
In the LXX
The Greek verb βάπτω occurs 16 times in 16 verses in the LXX. However, unlike טָבַל, it does not occur in Gen. 37:31 or 2 Kings 5:14, but it does occur in Lev. 11:32 wherein it translates a conjugation of the Hebrew verb בָּא (ba), as well as Psa. 67:245 wherein it translates a conjugation of the Hebrew verb מָחַץ (machatz).
On the other hand, the Greek verb βαπτίζω occurs 4 times in 4 verses in the LXX: 2 Kings 5:14, Isa. 21:4, Judith 12:7, and Sirach 34:25. In Isa. 21:4, it is used in the sense of “overwhelm” to translate a conjugation of the Hebrew verb בָּעַת (baʿat).6
In the Greek New Testament
The Greek verb βάπτω occurs 3 times in 3 verses in the 1550 Textus Receptus, and it is translated in the 1769 ed. of the KJV in all 3 occurrences by the English verb “dip.”7 On the other hand, the Greek verb βαπτίζω occurs 86 times in 65 verses in the 1550 Textus Receptus. It is predominately translated by a conjugation of the English verb “baptize.”
On the distinction between the verbs βάπτω and βαπτίζω, perhaps most often quoted is the physician Nicander of Colophon (Νίκανδρος ὁ Κολοφώνιος; 2nd c. B.C.), who himself was cited by Athenaeus in The Deipnosophists (Δειπνοσοφισταί). Athenaeus wrote,8
But they also ate as an appetizer turnips done in vinegar and mustard, as Nicander plainly shows in the second book of the Georgics; for he says: “Of turnip and cabbage, in truth, two families appear in our gardens, long and solid. The latter you wash and dry in the north wind, and they are welcome in winter even to the idle stay-at‑homes; for soaked in warm water they come to life again. But the other, the turnip roots, you cut in thin slices, gently cleaning away the undried outer skin, and after drying them in the sun a little, either dip (ἀποβάπτων) a quantity of them in boiling water and soak (ἐμβάπτισον) them in strong brine; or again, put equal parts of white must and vinegar in a jar together, then plunge the slices in it, having dried them off with salt.”
ὅτι δ᾽ ἤσθιον διὰ ἀναστόμωσιν καὶ τὰς δι᾽ ὄξους καὶ νάπυος γογγυλίδας σαφῶς παρίστησι Νίκανδρος ἐν δευτέρῳ Γεωργικῶν λέγων οὕτως: γογγυλίδος δισσὴ γὰρ ἰδ᾽ ἐκ ῥαφάνοιο γενέθλη μακρή τε στιφρή τε φαείνεται ἐν πρασιῇσι. καὶ τὰς μὲν θ᾽ αὕηνον ἀποπλύνας βορέῃσι, προσφιλέας χειμῶνι καὶ οἰκουροῖσιν ἀεργοῖς: θερμοῖς δ᾽ ἰκμανθεῖσαι ἀναζώουσ᾽ ὑδάτεσσι. τμῆγε δὲ γογγυλίδος ῥίζας (καὶ ἀκαρφέα φλοιὸν ἦκα καθηράμενος) λεπτουργέας, ἠελίῳ δὲ αὐήνας ἐπὶ τυτθὸν ὁτὲ ᾿ν ζεστῷ ἀποβάπτων ὕδατι δριμείῃ πολέας ἐμβάπτισον ἅλμῃ, ἄλλοτε δ᾽ αὖ λευκὸν γλεῦκος συστάμνισον ὄξει ἶσον ἴσῳ, τὰς δ᾽ ἐντὸς ἐπιστύψας ἁλὶ κρύψαις.
The History of Pre-Christian Baptism or Immersion
Immersion for Restoring Cleanness/Purity (טָהֳרָה)
Sirach 34:25 references the practice of immersion or “baptism” when it describes those who touched corpses as later baptizing themselves or being baptized (βαπτιζόμενος).
If a man washes after touching a dead body, and touches it again, what has he gained by his washing? RSV
βαπτιζόμενος ἀπὸ νεκροῦ καὶ πάλιν ἁπτόμενος αὐτοῦ, τί ὠφέλησεν ἐν τῷ λουτρῷ αὐτοῦ
According to the Torah, an Israelite who contacts a corpse is rendered unclean for seven days. In Num. 19:11, it is written,
He who touches the dead body of any soul of a man, then he shall be unclean seven days.
הַנֹּגֵעַ בְּמֵת לְכָל נֶפֶשׁ אָדָם וְטָמֵא שִׁבְעַת יָמִים
Moshe ben Maimon reiterated the process required to become clean (restore purity) after contacting a corpse (cp. Num. 19:12–19). In the Mishneh Torah, he wrote,9
How is a person, unclean from a corpse, made clean by the water of separation? A clean man takes three stalks of hyssop and binds them with one bond. Each stalk should have at least one bud. He should immerse the top of the buds in the water of separation while it is in a vessel, focus his intent, and sprinkle it on the [unclean] man or [unclean] vessels, on the third day and on the seventh day after sunrise. If one sprinkled after dawn, it is acceptable. After the water has been sprinkled upon it on the seventh day, he should immerse in a mikve during the day, wait until nightfall, and then, in the evening, he is clean.
כֵּיצַד מְטַהֲרִין טְמֵא מֵת בְּמֵי נִדָּה: לוֹקֵחַ אָדָם טָהוֹר שְׁלוֹשָׁה קְלָחִין שֶׁלְּאֵזוֹב, וְאוֹגְדָן אֲגֻדָּה אַחַת, וּבְכָל בַּד וּבַד גִּבְעוֹל אֶחָד. וְטוֹבֵל רָאשֵׁי גִּבְעוֹלין בְּמֵי נִדָּה שֶׁבַּכְּלִי, וּמִתְכַּוֵּן וּמַזֶּה עַל הָאָדָם אוֹ עַל הַכֵּלִים, בְּיוֹם הַשְּׁלִישִׁי וּבְיוֹם הַשְּׁבִיעִי, אַחַר שֶׁתָּנֵץ הַחַמָּה; וְאִם הִזָּה מִשֶּׁעָלָה עַמּוּד הַשַּׁחַר, כָּשֵׁר. וְאַחַר שֶׁיַּזֶּה עָלָיו בְּיוֹם הַשְּׁבִיעִי, טוֹבֵל בַּיּוֹם; וּמַעְרִיב שִׁמְשׁוֹ, וַהֲרֵי הוּא טָהוֹר לָעֶרֶב.
After being sprinkled with the “water of separation” (created with the ashes of the red heifer) on the third and seventh day of his uncleanness, the Israelite was to “wash his clothes and bathe in water” (וְכִבֶּס בְּגָדָיו וְרָחַץ בַּמַּיִם), and then he would be clean after sunset (cp. Num. 19:19). The Hebrew text does not use a conjugation of the verb טָבַל (taval) to describe the act of bathing in water, but rather, a conjugation of the verb רָחַץ (rachatz).
The Hebrew Verb רָחַץ
The Hebrew verb רָחַץ occurs far more often than טָבַל in the Hebrew Tanakh, 72 times in 71 verses. While it is often translated as “wash” and sometimes as “bathe,” the act of bathing consisted of immersing in a mikve (pool of water) in order to become clean after contracting uncleanness (i.e., becoming unclean).
The Mikve (מִקְוֶה)
In the Mishneh Torah, Moshe ben Maimon wrote,10
All unclean things - whether humans or vessels, whether they were defiled with a severe uncleanness according to the Torah, or whether they were defiled with uncleannesses according to the words [of the rabbis], do not become clean except by immersion (טְבִילָה) in water that is collected in a pool.
כָּל הַטְּמֵאִים--בֵּין אָדָם, בֵּין כֵּלִים, בֵּין שֶׁנִּטְמְאוּ בְּטֻמְאָה חֲמוּרָה שֶׁלַּתּוֹרָה, בֵּין שֶׁנִּטְמְאוּ בִּטְמָאוֹת שֶׁלְּדִבְרֵיהֶם--אֵין לָהֶן טַהְרָה, אֵלָא בִּטְבִילָה בְּמַיִם הַנִּקְוִים בַּקַּרְקָע.
The water that is collected in a pool is also known as a מִקְוֶה (mikve). There was, as can be expected, laws pertaining to the mikve and how to properly immerse therein.
In the Mishneh Torah, Moshe ben Maimon also wrote,11
Everywhere that the bathing of one’s flesh or the washing of one’s garments from uncleannesses is stated in the Torah, it is nothing but the immersion of the entire body in a mikve.
כָּל מָקוֹם שֶׁנֶּאֱמָר בַּתּוֹרָה רְחִיצַת בָּשָׂר וְכִבּוּס בְּגָדִים מִן הַטְּמָאוֹת, אֵינוּ אֵלָא טְבִילַת כָּל הַגּוּף בְּמִקְוָה
Accordingly, immersion (“baptism") or טְבִילָה was required for lepers,12 people and objects that contacted seminal fluid (e.g., during sexual intercourse or from a nocturnal emission),13 the nidda or menstruant,14 and so and so on. It is regarding all these baptisms or immersions that the author of the Epistle to the Hebrews wrote,15
concerned only with foods and drinks and various baptisms, and carnal ordinances imposed until the time of reformation.
μόνον ἐπὶ βρώμασιν καὶ πόμασιν καὶ διαφόροις βαπτισμοῖς καὶ δικαιώμασιν σαρκὸς μέχρι καιροῦ διορθώσεως ἐπικείμενα
Regarding the Greek phrase «διαφόροις βαπτισμοῖς» (“various baptisms”) in Heb. 9:10, Franz Delitzsch wrote,16

Immersion of a Convert/Proselyte to Judaism
Aside from being used to remove physical uncleanness (טֻמְאָה), baptism or immersion was one of three requirements for the conversion of a proselyte to Judaism.17
In the Babylonian Talmud, it is written,18
Derive from it that one is not a convert until he is circumcised and immerses.
וש"מ אינו גר עד שימול ויטבול
The requirement for immersion of a proselyte was derived from Exo. 24:8 since אין הזאה בלא טבילה, that is, “There is no sprinkling [of blood] without immersion [beforehand].”19 It is reasoned that when the mixed multitude entered the covenant, they had immersed before they were sprinkled with the blood by Moses. This conversion made one “like a newborn child.”20
Footnotes
1 There is also another noun, βάπτισις, that shares a similar meaning, although it occurs seldomly. See Josephus. Jewish Antiquities. Book 18, §117. Like English, Latin also possessed loanwords such as baptisma, baptismum, and baptismus.
2 Vol. 1, p. 147
3 p. 317
4 p. 516–517
5 Psa. 68:23 in the KJV.
6 See BDAG, p. 165, βαπτίζω, 3. c.; LSJ, p. 305, βαπτίζω, under "transf."; Thayer, p. 94, βαπτίζω, I. 3.
7 There is also a related verb, ἐμβάπτω, which also occurs 3 times in 3 verses.
8 p. 183, Book IV, Ch. 11
9 Sefer Tahara, Hilkhot Para Aduma, Chapter 11, Halakha 1
10 Sefer Tahara, Hilkhot Mikvaot, Chapter 1, Halakha 1
11 Sefer Tahara, Hilkhot Mikvaot, Chapter 1, Halakha 2
12 Lev. 15:2–13
13 Lev. 15:16
14 Lev. 15:19–24
15 Heb. 9:10
16 p. 73
17 The three requirements are: circumcision, immersion, and offering a sacrifice (this requirement was only mandatory when the Temple existed).
18 Seder Nashim, Tractate Yevamot, Gemara, Chapter 4, Folio 46b
19 Seder Nashim, Tractate Yevamot, Gemara, Chapter 4, Folio 46b
20 Seder Nashim, Tractate Yevamot, Gemara, Chapter 4, Folio 48b: רבי יוסי אומר גר שנתגייר כקטן שנולד, that is, "Rabbi Yose said, 'A proselyte that converts is like a newborn child."
References
Arndt, William; Bauer, Walter; Danker, Frederick William. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: U of Chicago P, 2000.
Athenaeus. The Deipnosophists. Books VIII-X. Trans. Gulick, Charles Burton. Cambridge: Harvard UP, 1969.
Dale, James Wilkinson. Classic Baptism: An Iniquiry into the Meaning of the Word ΒΑΠΤΙΖΩ, as Determined by the Usage of Classical Greek Writers. Philadelphia: Rutter, 1867.
Dale, James Wilkinson. An Iniquiry into the Usage of ΒΑΠΤΙΖΩ, and the Nature of Judaic Baptism, as Shown by Jewish and Patristic Writings. 3rd ed. Philadelphia: Rutter, 1873.
Delitzsch, Franz. Commentary on the Epistle to the Hebrews. Vol. 2. Trans. Kingsbury, Thomas L. Edinburgh: Clark, 1872.
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Jastrow, Marcus. A Dictionary of the Targumim, the Talmud Babli and Yerushalmi, and the Midrashic Literature. London: Luzac; New York: Putnam, 1903.
Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. Vol. 1. New York: Elsevier, 1966.
Liddell, Henry George; Scott, Robert; et al. A Greek-English Lexicon. 9th ed. Oxford: Clarendon, 1940.
Moshe ben Maimon. Mishneh Torah (מִשְׁנֵה תּוֹרָה). Ed. Mechon-Mamre. Jerusalem: Mechon-Mamre, 2015.
Thayer, Joseph Henry. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Rev. ed. New York: American Book, 1889.