A fat quarter of fabric is a 1/4 yard piece measuring approximately 18 inches by 22 inches. A regular quarter of fabric is a 1/4 yard piece measuring 9 inches by 44 inches. The larger dimension in each case varies if the fabric is not 44 inches wide.
A fat quarter is created by cutting 18 inches from a 44 inch wide roll of fabric and then cutting that piece in half. Quilt shops usually offer a selection of pre-cut fat quarters for sale.
Many crafters find fat quarters easier to handle and store than regular quarters. Fat quarters are often used for sampler quilts and scrap quilts and may be more versatile for patchwork and appliqué.