There are many ways that administrators monitoring servers help with overall system performance, but many of them boil down to some fundamental ideas about how servers work within a network.
Essentially, administrators look at servers to see how they handle various kinds of information requests. This has to be done in specific ways, to make sure that the monitoring software is actually picking up what's happening for end-users. By understanding whether servers are up and responding to requests, administrators figure out how long it takes for a request to go through, what kinds of results outside users see, and how network workloads are being handled in real-time.
For example, administrators may use a simple ping test to see how servers respond. They may check various server ports or perform in-depth user testing to simulate user demands. In a consumer-facing system, this helps them to figure out whether individual web site visitors will be able to navigate sites without getting error messages from a database. These are some of the practical ways that server monitoring helps to make sure that networks deliver all of their intended services to a user audience.