What is it called when computers are connected and operate through one main computer?

If you mean in networking, it would be a client/server network, with the main computer being the server, which would manage data transfers in the network and stuff like that, and the clients would be the regular computers; usually the computers that people would be using to work on often (whereas a server tends to be idle a lot of the time, only operated by technicians of wherever the network is located (school, business etc.)).