An ATC is an artist trading card. These are little cards which measure 2 ½ X 3 ½ inches (63 mm X 89 mm). They can be made from anything, using any technique. Most people make them from paper; other people (like me) make them from fabric. I've also see ATCs made from wood, metal, yarn, plastic, and clay.
Anybody can make ATCs. There are only two rules: the first is the size. The second rule is that the cards must be traded or gifted, never sold.
There are many places online where you can trade ATCs. My current favorite is Swap-Bot.