A fat quarter is a quarter-yard of fabric as the name implies, but rather than being cut off the bolt at the standard 9" long for a quarter-yard, it is actually a half-yard of fabric cut in half so each piece is 18" x 22", which is a more useable shape than a long, narrow strip.
Fat quarters are often sold in bundles of coordinating fabric which I find to be very helpful, because the matching is already done and you can be secure in the knowledge that all of the prints will go with each other nicely for whatever project you have in mind. Below, I have shown just a couple of examples of fat quarter bundles that can be purchased online at Fabric.com. If you do not like the colors or styles shown, there are many, many more assortments available.
Here are some suggestions for easy fat quarter projects to make using one or more fat quarters including some links to free patterns! Coffee Cozy, iPod/Camera Cozy Tutorial, Pincushions, Quilted Coaster Set, a little boxy pouch, sachets, placemats (these would be fun to mix-and-match using a bundle), fabric postcards, handbags, baby or doll quilts, table runner, and a pillow. This simply scratches the surface! For more ideas, check the internet or you can purchase one of the books shown below with projects designed specifically for fat quarters!