Nowadays, server functionality has become so rich, complex and varied in nature that there are whole very powerful computers dedicated to being exclusively servers. This has led many non-technical people to denote servers as being machines that run services.
Generally speaking, a server is a machine with a specific set of programs that offer different types of service, which other machines (then called clients) request to do certain tasks. For example, a file server is a machine which keeps files, and allows clients to upload and download them from it. A web server is a machine that hosts web sites and allows Internet users (clients) to access these web sites. The page you are reading now comes from the about.com web server. A mail server is a machine which, along with the storage and management of email messages, provides service to email users who can read, retrieve, and manage these emails messages.