First, some background information.
1. Fabric yardage on a bolt is folded in half. When you unfold that fabric it measures around 44″ (it varies) from selvage to selvage.
2. A quarter of a yard is 9 inches.
This means a quarter yard of fabric is 9 x 44 inches. If you want your quarter cut “fat” though, you can instead have your fabric cut at 18 x 22 inches. This is done by cutting a half yard of fabric, and then cutting along the fold to create a “fat quarter” of a yard rather than the skinny quarter you would otherwise get.