What is a MIME type?

A MIME type is a label for a given type of data so software can know how to handle the data. It serves the same purpose on the Internet that file extensions do on Microsoft Windows.
So if a server says “This is text/html” the client can go “Ah, this is an HTML document, I can render that internally”, while if the server says “This is application/pdf” the client can go “Ah, I need to launch the FoxIt PDF Reader plugin that the user has installed and that has registered itself as the application/pdf handler.”