Layers is a multi-definition term, depending upon the context of use in Cinema 4D. At its root definition, a layer is some sort of container, and it may hold geometry, scene objects such as cameras and lights, and other information. For modeling purposes, the layer is how you can choose to organize all of your data that you use to build your objects. You can create assemblies that you manage by layers, or you can put your contruction work into layers that will be discarded layer as your final geometry goes into a different layer.
For animation purposes, you may have different objects in different layers, and/or you may have different levels of animation in separate layers for further control. In addition, if you can’t decide on a particular action or interpretation, you can put different “takes” into separate layers, and play with them until you get what you want.
For rendering, you may need to output different types of images for later use in compositing. The rendering system is layer-friendly, and Cinema 4D has quite a bit of versatility here.
For compositing, its all about layers. Here, layers are pretty much the same as you would have in Adobe Photoshop and Adobe After Effects. Many times its advantageous to break out a shot into layers to save on rendering time and to allow for further control and manipulation.