A Virtual private server (VPS) is a server that does not directly exist as a single computer, but is emulated on a computer together with other virtual servers. This means that they are usually cheaper because they share the resources with other servers. The good thing about this is that you (the admin) have (almost) complete access to the server. You can install whatever OS you like and have complete root access, which enables you to change almost everything. In contrast to a hosting arrangement, where you only can host websites.
The reason why I am renting one is so I can play around with it It is wonderful fun. During the last couple of months I have set up multiple services on it, which I briefly describe now: