The Jaredites are a group of people who left the middle east area at the time of the Tower of Babel. They were led by Jared and his brother (Mohonri Moriancumer), and the group included family and friends of Jared and his brother.
Knowing that the languages would be confounded, Jared asked his brother to pray to the Lord so that he would not confound their language and the language of their friends. The Lord granted their request. Jared also asked his brother to inquire of the Lord if they would depart that land and go another land. The Lord told the brother of Jared that he would send them to another land, a choice land, a land of promise. Jared, his brother, their friends and families gathered food, seed, flocks, honeybees, birds, and other items and were led into the wilderness where they traveled many years. They came upon a seashore where they made eight barges and traveled across the sea to a promised land, somewhere in North, South, or Central America.
The route of their travels is unknown and where exactly they landed and lived is unknown. They were here in the American continent from approximately 2100 BC to 600 BC, about 1500 years. During that time, they may have spread out in both continents, right now, no one really knows. I personally believe that at least many of them lived on the North American continent, mainly in the Heartland (middle North America), and possibly had their last great battle in the upstate New York area. I have no scientific or religious backing for that, that is just my personal belief.
Please read more about the Jaredite people in the Book of Ether, in the Book of Mormon. There is not much written about them, but enough written to demonstrate how the Lord blesses his people when they are righteous and faithful, and follow His commandments, and how an entire civilization can be destroyed by disobedience to His laws.
You can visit Mormon.org to learn more about the Book of Mormon.