A fat quarter is a patchwork and craft sizing terminology that you will often come across when looking for cotton fabric.   It is different to the cut you will get in a conventional fabric store, and allows scope for larges pieces of fabric to be cut fromthe quarter to use in your patchwork, craft and applique projects.  

I have put together this graphic to show the difference, I hope it helps:

In metric, at Fat Quarter measures approx 45 x 55 cm. 

In imperial, a Fat Quarter measures approx 18” x 22”.