Map region is the data, Simulator is the program that runs it, server is the hardware that holds both and talks to you. Each one has to be hosted on a server running copies of the Simulator program (one simulator per region, 4 or more sims per server, 8000 or so servers). There are about 29,000 regions in total currently.
Map regions are all 256x256 meters in size horizontally by 4096 meters vertical (the build limit, you can fly higher, but not place objects above that). Map Region - The basic unit of the Second Life world is a map region. The Main Grid (Agni) - Click for enlarged view Map Terms