A layer is a piece of geographic data (such as an image, scenario output, shape file, etc), presented in a graphical form and rendered on a map, positioned to its extent (bounds).
A map can have many layers, which are listed and managed in the Layers Panel. On the map, layers are rendered from the top layer in the Layers Panel to the bottom layer in the Layers Panel. Layers that are rendered further down in the list can cover the contents of the layers that were rendered before it. Normally you would order layers, so country raster layers are rendered first, then state/regional raster layers are rendered next and finally shape/vector files are rendered last.