Fat Quarters refer to a particular cut of fabric quilters often buy. I thought it was a fancy term for left-overs from a bolt of cloth, but after you asked I looked it up and discovered it has a more precise meaning. A fat quarter is a quarter-yard of fabric cut not into one 1/4 yard strip, but rather a yard of fabric cut into 4 equal-sized pieces, by cutting once (in the middle) width-wise then again height-wise.
Or, to quote from http://quilting.about.com/od/stepbystepquilting/ss/fat_quarters.htm
"A fat quarter is a one-fourth yard cut of fabric that (usually) measures 18" x 22" instead of the typical 9" x 44" quarter-yard cut. The longest side's dimension will vary if your fabric is not 44" wide."
There's an explanatory illustration on the about.com page if you need help deciphering what I've said.Edited at 2009-01-19 04:02 pm (UTC)