A server is simply a computer, not very different than the one you're using. It might look uglier, spit hot air, and only get touched once a decade, but it's still running an operating system and likely connected to the internet.
What's different is that instead of for consumers, servers are used to run code exclusively. A simple explanation of the cloud is a bunch of linked servers.
Servers can be configured for many different things, but common usages are to power websites and online services.