I have learned that in order to understand Scripture, it is necessary to find what other Scriptures there are to help decipher what is meant.
Usually this may only be checking the surrounding Scriptures and that will let you know what the intent is, but that alone is not always sufficient to extract its full meaning.
So let's examine Luke chapter 10 and see what help we can find there:
Luke 10:1 KJV
After these things the Lord appointed other seventy also, and sent them two and two before his face into every city and place, whither he himself would come.
According to this Jesus chose seventy others (which is generally accepted as other than the Apostles).
In verses 2 through 16 KJV
Jesus gave them specific instructions as to how they were to conduct themselves, ( this was most likely because he wanted them to display Christianity).
In verse 17 They returned:
Luke 10:17 KJV
And the seventy returned again with joy, saying, Lord, even the devils are subject unto us through thy name.
This shows some surprise at the fact that they could order around devils in the name of Jesus.
Immediately after that is when Jesus says:
Luke 10:18 KJV
And he said unto them, I beheld Satan as lightning fall from heaven.
This statement appears to be off subject, so why would Jesus say that at this particular time?
These people, (and we are not told that they are all men, and Jesus words would be equally pertinent to women as to men); would all be well versed in the scriptures; and would be aware of the following Scriptures; which have to do with Satan's fall from grace.
From glorified to profane:
Ezekiel 28:14 through 19 KJV
14 Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.
15 Thou wast perfect in thy ways from the day that thou wast created, till iniquity was found in thee.
16 By the multitude of thy merchandise they have filled the midst of thee with violence, and thou hast sinned: therefore I will cast thee as profane out of the mountain of God: and I will destroy thee, O covering cherub, from the midst of the stones of fire.
17 Thine heart was lifted up because of thy beauty, thou hast corrupted thy wisdom by reason of thy brightness: I will cast thee to the ground, I will lay thee before kings, that they may behold thee.
18 Thou hast defiled thy sanctuaries by the multitude of thine iniquities, by the iniquity of thy traffick; therefore will I bring forth a fire from the midst of thee, it shall devour thee, and I will bring thee to ashes upon the earth in the sight of all them that behold thee.
19 All they that know thee among the people shall be astonished at thee: thou shalt be a terror, and never shalt thou be any more.
From having access to heaven
Job 1:12 KJV
And the LORD said unto Satan, Behold, all that he hath is in thy power; only upon himself put not forth thine hand. So Satan went forth from the presence of the LORD.
1stKings 22:21 KJV
And there came forth a spirit, and stood before the LORD, and said, I will persuade him.
Zechariah 3:1 KJV
And he shewed me Joshua the high priest standing before the angel of the LORD, and Satan standing at his right hand to resist him.
So Jesus in view of Luke 10:17 and 18 Jesus was warning them not to get to puffed up, since that pride was the very thing which had caused even the Angel Lucifer to fall from grace and access to Heaven. This becomes clear in:
Luke 10:20 KJV
Notwithstanding in this rejoice not, that the spirits are subject unto you; but rather rejoice, because your names are written in heaven.