A computer that provides services to other computers on the same network. In the context of sharing an Internet connection, the server computer typically has 2 NICs and runs sharing software. It "serves" Internet access to one or more client computers.
Computer hardware and software capable of storing many files and making them accessible to users on the Internet. Web hosting companies rent space on their large servers to individuals and businesses. A block of 30 megs should cost about $10.00 a month. You can have your web files on your own computer but upload [save them] onto your server where they will be available to the world. It's usually a good practice to have your files in two locations, as a backup. If a catastrophe strikes the server you are renting and all your files are lost, the files on your own computer will be your backup. The converse of this is true.
A network device that provides a service to network users, such as shared access to a file system a file server, control of a printer a print server, or storage of messages in a mail system a mail server.