The user gets his or her own Web server and gains full control over it (user has root access for Linux/administrator access for Windows); however, the user typically does not own the server. One type of dedicated hosting is self-managed or unmanaged. This is usually the least expensive for dedicated plans. The user has full administrative access to the server, which means the client is responsible for the security and maintenance of his own dedicated server.
It shouldn't come as any surprise that, like other web host providers, A2 Hosting's unlimited plans aren't actually unlimited. It expect you to use its service like "similarly situated customers." This is like being on a highway. If everyone is going a few miles above the speed limit, you're probably okay, but if you're barreling down the fast lane past everyone else, you're probably going to be asked to slow down.