Mime types tell browsers how to handle specific extensions.
For example, the text/html mime type equates to .htm, .html, and .shtml extensions on most servers, and this tells your browser to interpret all files with those extensions as HTML files. You can alter or add new mime types specifically for your site (note that you can not alter the system defined mime type values).
MIME types are often used to handle new technologies as they appear. When WAP technology first appeared, no one had these extensions set up on their server. However, with mime types you could have set it up yourself and begun serving WAP pages immediately.