The user gets his or her own Web server but is not allowed full control over it (user is denied root access for Linux/administrator access for Windows); however, they are allowed to manage their data via FTP or other remote management tools. The user is disallowed full control so that the provider can guarantee quality of service by not allowing the user to modify the server or potentially create configuration problems. The user typically does not own the server. The server is leased to the client.
Many services offer a low "starting price," but require you to prepay for two or three years of service to get that price. After the promotional period, the renewal price for some services can be two, three, or even four times the initial promotional pricing. While the initial deal might be incredible, the cost of transferring your site (or paying the added fee) in a couple of years may be something to consider.