or file server: A machine that provides files via a network. Perhaps because of time spent working on BITNET, I tend to use it as a synonym for mailserver, or a machine that returns files that are requested via email.
a computer on the network running special software so that it can provide network services, such as file transfer from its disk space, to other clients on the network.
Sometimes the client will need to download files, usually workers or targetfiles. These are provided by a so-called fileserver, which is usually just an HTTP or FTP server running at the same (or another) machine than the main server.