Fabric cutting details - What is the "nap" of a fabric and why it cutting the fabric correct important?

“With nap” means that you lay out the pattern pieces on the fabric before you are cutting the fabric in the SAME direction, so not how it is in the picture above, where one panel is laid out in one direction and the other in the opposite direction. 

To determine what a fabric's nap is, all you have to do is touch it. Think of a corduroy or a velvet, it will feel smooth when "padding" it in one direction and not so much when "padding" it in the opposite direction. The nap in a finished garment usually feels smooth when you "pad" the fabric downward. The nap is also important with how the light hits it, so both the front and back panels should have the nap going in the downward direction.