About 300 million years ago, near the end of the Carboniferous period, when the first reptiles were evolving, the tectonic plates began to form the supercontinent of Pangaea. When the Euramerica continent smashed into Godwanaland, that pushed up the land to make the Appalachian mountains.
More about the Appalachian Mountains
The Appalachian mountains are among the oldest mountains in the world. They have eroded over the years, so they aren't very high anymore, and they don't even have snow on them in the summertime. The Appalachians are about the same age as the Ural mountains that separate Asia from Europe, but they are far older than the Alps, the Himalayas, the Rockies, or even the Andes, which are the next oldest major mountains.