Server-side applications are programs that run on the machine that your website sits on. There are no limits to what they can do or the language they are written in.
Their usual purpose to to provide pages that depend on some form of user input, processing forms, interacting with databases and email handling. For example, when you log on to an online bank you give a password and username, choose the account and time period to look at and a page of transactions appears on your browser. All of this processing is done by server-side applications mediating between your input (password, etc) and a database on that server.
You may use them to