The Book of Mormon tells of the Nephites and Lamanites, but it wasn't written for them. In fact, many of the Book of Mormon prophets knew that future generations would have the book (see, for example, Mormon 8:35). Near the end of the Nephite civilization, the Lord inspired Mormon to choose from the many records of his people the teachings and accounts that would be helpful to us today.
The main purpose of the book is to teach and testify of Jesus Christ. His gospel, which is taught clearly and powerfully in the Book of Mormon, applies to our day, as it does in any age. But even the events and story lines of the Book of Mormon can teach us. For example, if you look at the enemies and wars in the Book of Mormon as symbols for the spiritual battles we face today, you can learn how to strengthen yourself against temptation.
As you prayerfully study the Book of Mormon, your faith and testimony will be strengthened—and that is something we all need today.