If you've ever sewn anything, you've probably noticed that there are two main types of fabrics: napped and non-napped. Napped fabric has a fuzzy surface, while non-napped fabric does not. The term nap refers to the direction in which the fibers lie on the surface of the fabric. When you stroke your hand along the nap of a fabric, the fibers should all lie in the same direction.
The nap of a fabric can affect how it looks when it's made into clothing or other items. For example, a velvet dress will look different if you view it from different angles because of the way light reflects off the surface. The nap also affects how a pattern appears on fabric. A plaid pattern, for instance, will look different depending on which way you stroke your hand across the fabric (i.e., with or against the grain).
Some fabrics are meant to be used with their nap running in a particular direction. Others can be used either way; it just depends on the desired effect. When cutting out patterns, you'll need to pay attention to which way the nap is running so that everything lines up correctly when you sew it together. Otherwise, one side of your garment might end up looking noticeably lighter or darker than the other side!