A Fat Quarter or  FQ is 1/4,  or one quarter of a yard, only cut on the half yard,
so instead of being 9" by 44" as it normally would be cut in a fabric shop,
it measures approximately 18" by 22".
 Many quilters and crafters prefer this cut.  It is the same amount of fabric but instead of fabric being narrow and long,  9" x 44", it is twice as wide and half as long, 18" x 22".

Many internet sites sell yardage by the Fat Quarter.   Hence, a quarter yard being the smallest cut, if you want running yardage you order the number of quarters you need.  For example, if you want 1 yard of fabric, you order 4 quarters. If you want 2 1/2 yards of fabric you order 10 quarters, etc.