At the end of the Book of Mormon, the Nephites and Lamanites had a huge war, and all the Nephites were destroyed. (See Mormon chapters 6-8) That left only the dark-skinned Lamanites on this continent. We believe that the Lamanites are the ancestors of the Native Americans.
After all of his people were destroyed, Moroni was the only Nephite left. He finished engraving his record upon the gold plates, and buried them. (see Moroni 10) These gold plates were delivered by an an angel to Joseph Smith in 1827, and he translated them and published them as the Book of Mormon (see Testimony of the Prophet Joseph Smith).