From the very title page:
... And also to the convincing of the Jew and Gentile that Jesus is the
Christ, the Eternal God, manifesting himself unto all nations— ...
...to the last page of the record (Moroni 10:32-33):
32 Yea, come unto Christ, and be perfected in him, and deny
yourselves of all ungodliness; and if ye shall deny yourselves of all
ungodliness, and love God with all your might, mind and strength, then
is his grace sufficient for you, that by his grace ye may be perfect
in Christ; and if by the grace of God ye are perfect in Christ, ye can
in nowise deny the power of God.
33 And again, if ye by the grace of God are perfect in Christ, and
deny not his power, then are ye sanctified in Christ by the grace of
God, through the shedding of the blood of Christ, which is in the
covenant of the Father unto the remission of your sins, that ye become
holy, without spot.
... the Book of Mormon espouses the doctrine of Christ: His gospel, ministry, and everlasting Atonement:
For another instance, 2 Nephi 33:10:
10 And now, my beloved brethren, and also Jew, and all ye ends of the
earth, hearken unto these words and believe in Christ; and if ye
believe not in these words believe in Christ. And if ye shall believe
in Christ ye will believe in these words, for they are the words of
Christ, and he hath given them unto me; and they teach all men that
they should do good.
However, the overall focal point would be in 3 Nephi, chapters 11-28, which records the Savior's ministry upon the American continent. I have seldom seen Book of Mormon passages referenced in an introductory setting more than those which directly speak of Jesus' gospel: faith, repentance, etc.
The Book of Mormon repeats the same doctrine over and over but in different ways... so it's hard to pinpoint a specific verse to answer your question. Typically, missionaries will probably invite you to read in 3 Nephi about Jesus' visit to the Americas, or in 2 Nephi 31 where Nephi preaches on faith, repentance, baptism, and remission of sins.
Which passage missionaries assign people to read is chosen on an individual basis. To explain Christianity in a nutshell, they would probably refer you to John 3:16 in the Bible (it is an excellent verse) -- to explain Mormonism in a nutshell, it varies between any of these types of passages, depending on who you are and your situation.