I've heard them called helpers and pushers. Around Roanoke, VA, on NS (former N&W) it seems that a pusher is an assigned job, pushing trains over a grade. Helpers are power from other trains, pressed into service to help a stalled train. Minor difference, and it's not spelled out anywhere, just an impression I get.
As to why, 4 large diesels have enough tractive effort to break a standard knuckle in a dead pull. Most coal train I've seen use high tensile strength knuckles, which is why we are allowed to use 4 engines on them. Even so, the slightest jerk can still easily break a knuckle. So if more power is needed, it has to be put somewhere besides the head end. Also, keeping pushers on the rear makes it easier to remove them at the top of the hill.
There are also distributed power units, which are radio contriolled from the head end. They're a fixed part of the consist of the train, staying with it for the entire trip. Southern, and I believe a number of other RRs, tried them 20-30 years ago, but eventually abandonded them. I believe there were problems keeping them synchronized with the head end. Newer GE units have a (hopefully new and improved) DP system built in, and it seems to be working better than in the past.