Content-wise, not much of our unique doctrine and theology come from the Book of Mormon; most of it is found in the Bible.
One of the primary reasons for the Book of Mormon, according to the book itself, is to testify of the Bible - and to open our minds and hearts to the possibility of communing directly with God. I think the Book of Mormon acts as a catalyst to force someone to humble himself/herself to approach God with a sincere heart and ask for personal revelation. Those who receive a "witness" begin a journey of openness to the Spirit, which is symbolized (and sometimes actualized) in the Gift of the Holy Ghost. That process (companionship) opens the mind to read the Bible with new eyes, through which the truly unique doctrines of the Restoration are suddenly understood.
It also opens a conduit to seek personal revelation in personal areas - at the individual level, which, when you think about it, is what keeps many people who struggle with their faith active in the Church. They received a personal witness of some strength when they opened their heart to the possibility of communing directly with God, and the Book of Mormon played a huge role in that for many.