Suburban or Commuter Rail, is a passenger rail transport service that primarily operates within a metropolitan area, connecting commuters to a central city from adjacent suburbs or commuter towns. Would say is mainly above ground, hope that helps
To extend and hopefully help. First, the academic part... like Jamie explained, it's the "outer ring" of a (big) city where people have their homes. Languages can have different terms for it, my own is actually calling it pre-city, the perspective of approaching from the countryside. Sometimes it's a closed system, while other times its just a frequently stopping, often shorter service on a long distance line. In TSC, old GWML is a great example, as you gradually approach from Oxford, you can observe an increasing density of human dwellings. From your name I guess American interests. The most obvious places to go would be California (Pacific Surfliner, Peninsula Corridor, Sacramento Northern), and pretty much the entire MTA ecosystem: Metro-North, North Jersey Transit, Springfield, Hudson Line... But also Miami-WPB with its commuters, or the Chicago area.