Client/server in the domain of a database management system refers to how information is processed to fulfill a request. With typical systems, your computer queries the database for an entire set of records, then sorts through the results to determine what information it wants to keep to answer your request.
With client/server, your system, the client, creates the request. The request is sent to the server, which focuses on the best way to answer the request. Once the information has been put together to answer the request, the entire package of results is returned. Only those results that correspond to the request are returned, ready to be used immediately by the client application.
The client/server concept is similar to realizing you need a file from a file cabinet down the hall. You have two choices: You can have the file cabinet wheeled to your office where you can sort through the files manually, or you can simply request the specific file you need, then have someone retrieve only that single file and return it to you. This latter scenario is typical of a client/server situation.