Think of layers as sheets of paper - only those sheets of paper are cut into different shapes. You might have a sheet shaped like a circle placed on your desk; that's one layer. If you add a sheet shaped like a square, that's another layer. The square might overlap the circle and obscure part of it, or not, but it's still a separate layer.
Working with layers in animation and graphics software lets you composite your scenes in a way that doesn't require fitting everything together perfectly in each frame; you can use layers to give you more freedom in editing, and also to keep from merging objects together on one frame when you need them to be separate in others. Layers can also be rearranged, allowing you to change the order in which objects are displayed, thus changing the composition of your scene.