Server based Computing is a concept used to describe the process of a server acting as the processing system for a number of clients.
A number of dumb terminals or systems without processing power are attached to a main server that allows these clients to use the data on the server and act upon it.
The server is the central process for all these clients. Server based computing also means that the entire system is centralized.
Generally, mainframes and high performance servers fill this role in an enterprise and from a number of clients the data can be queried upon, processed and with the right permissions can be modified.