Quilling is a paper art where you coil up thin strips of quilling paper around a slotted quilling tool (or a needle tool) and then make shapes from the coiled paper. You can make some cool quilled designs like flowers, lettering, animals, people, trees, other items, etc. Basically anything you can think of you can make with quilled shapes once you learn all the basic quilling shapes and know how to put them together correctly using the right length of quilling paper strips. You need a few supplies to start quilling; such as a quilling tool, paper strips, paper glue, and possibly a circle sizer (to be sure your coils are the same size for some patterns.)
Its a great way to embellish scrapbook pages and add designs to card making. Also I've seen quilling as a stand alone art where you can frame it or add it to a glass/plastic jar or otherwise show it off.
Quilling is pretty neat because its really intricate and people will think you have spent a long time on it but it really doesn't take as much time as you'd think, if you enjoy crafts and want to make some cool things.
Its kind of hard to explain how to do but if you want to check out a free video, you can see one at http://www.LearnQuilling.com and they have a lesson on how to make a quilled flower. That might help so you can see if its something that you'd want to do. I think its pretty neat and a really fun "craft" or art, that a lot of people don't do because they might think its too difficult.
Anyway, hope that helps you understand quilling better and you get a chance to try it out soon! Have fun!