Dream catchers are an authentic American Indian tradition, from the Ojibway (Chippewa) tribe. Ojibway people would tie sinew strands in a web around a small round or tear-shaped frame--in a somewhat similar pattern to how they tied webbing for their snowshoes--and hang this "dream catcher" as a charm to protect sleeping children from nightmares. The legend is that the bad dreams will get caught in the web.
Traditionally Native American dream catchers are small (only a few inches across) and made of bent wood and sinew string with a feather hanging from the netting, but wrapping the frame in leather is also pretty common, and today you'll often see them made with sturdier string meant to last longer. During the pan-Indian movement in the 60's and 70's, Ojibway dream catchers started to get popular in other Native American tribes, even those in disparate places like the Cherokee, Lakota, and Navajo.