What's a layer?
A layer is basically a way to show multiple levels of information independent of each other. Layers are not just a mapping or cartography concept; graphic designers and digital artists make heavy use of layers.
Imagine a printed-out map of a city. Let's say you also have two sheets of transparent paper. One sheet has blue lines that indicate bus routes, and the other sheet contains green lines that indicate bicycle routes. Now, if you placed the transparent sheet of paper with bicycle routes on top of the map, you would see a map of the city with the bicycle routes outlined.
Putting on or taking off these transparent pieces of paper would be equivalent to turning a layer on or off. The order you place the sheets on top of each other also affects what the map will look like—if two lines intersect, you would either see the green line on top or the blue line on top. That's the basic concept of a layer.