Deep pocket sheets refer to the corners of a fitted sheet. Depending on the brand, some sheet sets can fit mattresses up to a certain thickness. Sheet sets with deep pockets are a nice feature if you have a bed taller than 12 inches or have a thick mattress pad. Fitted sheets should fit snugly over each corner, but not too tightly. If your mattress’s shape is slightly distorted from too-tight sheets, you need to choose a different size. Otherwise, you could damage the bed.