For Mormons, the Book of Mormon isn't one of the most important gifts in the history of world because it compares to the great literature or philosophy of the world or because it has objective historical worth. It is one of the most important gifts because it is how God has chosen in our day to testify that Jesus is the Messiah, our Savior.
As the frontispiece of the Book of Mormon shows, the Book of Mormon understands itself as part of the fulfillment of God's covenant with Abraham (cf. Abraham 2:9-11). (According to Mormon belief, all who come to Christ are of the house of Israel, whatever their genetic origins. They are heirs of Abraham's covenant.) Indeed, one of Joseph Smith's revelations tells us that the Book of Mormon is itself a covenant (D&C 84:57).
We sometimes speak of covenants as a species of contract or as the same as contract, but I think that's a mistake. Contracts are between persons who, in virtue of their contract, have a kind of equality. Contract is a kind of mutual promising. In contrast, a covenant with God is a relation of obligation to someone whose superiority over me is infinite.
Perhaps the best model for us to use to understand covenant is one often used in the Bible, the faithfulness of marriage. The marriage covenant is not like an ordinary promise. In ordinary cases, if I promise something, I have the right to know what I've promised. In fact, if it later turns out that I could not reasonably have known what I was promising, then I am justified in not keeping my promise. If I promise to buy a car from someone next week and, in the meantime, he or she wrecks it, I can justly refuse to honor my promise. In marriage, however, the promise is specifically a promise to do what one does not know. It is a promise that requires my loyalty to the promise, though I do not know and cannot know what that loyalty will require. Marital partners do not and cannot know what to expect, yet they promise to remain faithful. Religious covenants are like that: we agree to do what we do not yet know, but we agree because we trust our Father. That trust is faith.
Surely the most important function of scripture is to give our lives godly form. Joseph Smith taught that the Book of Mormon has that power more than any other scripture, whatever the superior literary, philosophical, and other merits of those other scriptures might be. Book of Mormon prophets like Abinadi and Ammon teach that the scriptures have the power to change our lives. As another Book of Mormon prophet, Alma, said, preaching the word has "a great tendency to lead the people to do that which was just—yea, it [has] more powerful effect upon the minds of the people than the sword, or anything else" (Alma 31:5). As we read, study, and ponder scripture diligently and faithfully, the Word becomes written in our hearts and we become different people. The Book of Mormon comes with the promise that it can do this at least as powerfully and effectively as any other scripture. Mormons believe it can do this because God specifically prepared, preserved, and presented it for our day.
Mormons believe that it is a great privilege to have been entrusted with the Book of Mormon. Just as Paul said that the best thing about being a Jew was that God's words had been entrusted to Jews (Rom. 3:1-2), perhaps the best thing about being a Latter-day Saint is that the Book of Mormon has been entrusted to us. We have received a gift and that gift was given to us so that Israel (in the broad sense mentioned above) might be restored to its inheritance, and so that all the world might receive the blessings of salvation.
While we wait on the fulfillment of that restoration, if Mormons live up to the responsibility that the trust and gift of the Book of Mormon brings, we will do as the book demands. We will wait on the restoration of Israel by bearing the burdens of our brothers and sisters, by mourning with those who mourn, comforting those who need comfort, and by standing as witnesses of the Father and the Son in the lives we lead (Mosiah 18:8-9).