Behold, my soul delighteth in proving unto my people the truth of the coming of Christ; for, for this end hath the law of Moses been given; and all things which have been given of God from the beginning of the world, unto man, are the typifying of him. 2 Nephi 11:4 (See 2 Nephi 25:16, 19 also)
The word "Christ" does not show up until the New Testament in the Bible, written during the first century AD.
"Christ" is a Greek word that means "anointed one" and appears 569 times in the New Testament.
The reason it does not appear in the Old Testament is because it's a Greek word and the Old Testament was written in Hebrew.
In 2 Nephi (second book of the Book of Mormon), written between 559-545 BC, the word "Christ" appears 35 times. The writer, Nephi, was a Jew.
The Greek language had been around as early as 1500 BC. The Ancient Greek language (800-330 BC) was spoken around this time, the same language used by Greek writer Homer (approximately 850 BC), but before Aristotle and Sophocles.
Around the time that Nephi apparently wrote this book, the Greek language had not spread to Israel until the Greeks invaded in 312 BC. Jews spoke Hebrew exclusively and had no reason to know and understand Greek words like those appearing in the Book of Mormon (for example "church" and "baptism").
Joseph Smith knew Christ as a New Testament word and inserted it freely in portions of the Book of Mormon before they historically would be known.