It sounds silly but a server is simply a computer running a service or services usually on a network. In most cases, it refers to a computer pretty much dedicated to simply running these services. Services include hosting a game, running the html pages for a website, running the email, providing security and authentication, storing and organizing centralized and shared files, running a big financial package or database and many more.
The complement (normally) to a server is a client. A client is a computer that is usually operated by a human (although not necessarily so in modern times). Think of a client as an end user of services.
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