There are two parts to the render layers settings. First is each render layer that you create, each of these results in a new rendered image that can be added into blenders compositor. Second is the passes that are used to make up the render layer, these are available as sockets in blender's compositor.
When you save the render result you will normally save the combined result as a 2d image, most image formats will only support this one flat output. However if you save the render result as OpenEXR multilayer, then you will get each render layer and associated passes in the one file. Depending on the level of OpenEXR support in your other application you should get access to each of these outside of blender.
Another option is to setup a File Output for each pass, this will let you save each chosen pass or layer as a separate image that can be used by any application. To do this you connect each desired socket to a File Output node in the compositor, use the properties panel N to access all settings for the file output node.