The word "server" has a broad definition in modern computing. In general, it can mean anything that serves anything onto a network. Most commonly, it refers to either a computer that serves data or files onto the Internet, or the software on said computer that enables this to happen. There are many different types of server software, and they often work in conjunction with each other.
Web Server Software
The most familiar type of server software serves a series of files on a computer onto the web in the form of a website. It is able to do this using the HyperText Transfer Protocol, or HTTP, a method through which web browsers request data from web servers and web servers respond with the data: usually a combination of HTML files and images. Popular web servers include Apache and Microsoft IIS.
FTP Server Software
While web servers use the HTTP, FTP servers use the File Transfer Protocol, which is the most common method for rapidly transferring large files across a network. FTP server software works in conjunction with FTP client software, programs designed for users doing the transferring. Common FTP servers and clients include Filezilla and Crush FTP.
Mail Server Software
Mail servers are programs that allow you to send and receive email. Unlike web or FTP servers, mail servers often use three different common protocols: SMTP (the Simple Mail Transfer Protocol), POP (the Post Office Protocol) and IMAP (Internet Message Access Protocol). POP and IMAP are used primarily for receiving mail, while SMTP can be used for sending or receiving. Common mail servers include Eudora and Mercury Mail.
Database Server Software
Database servers, as the title suggests, serve databases over a network. Databases provide content to the web: they can contain anything from articles to numbers to a member or product directory. Data server capability is often wrapped inside a Relational Database Management System (RDBMS), a set of programs that aid in the creation and maintenance of databases. Common RDBMSes include Oracle and MySQL.
Miscellaneous Server Software
Since a server is defined as any program that connects files to a network, servers don't necessarily have to aid in creating websites. iTunes and other audio programs use music servers that stream music between computers. Online games such as World of Warcraft use dozens of servers that allow users to log on and play. Instant messenging programs (with the exception of peer-to-peer programs, which cut out the server as a middle man) use servers as well.