When you purchase a Hosting account for example
www.hostgator.com you pay like idk $10/month lets say you are on a shared server with other sites running on it. Everyone shares the resources of the server which sometimes might cause it to be slow but rarely.
You can purchase a dedicated server for like $170/month and only your site will be running on it and it will be faster. Once your site gets bigger the Host will require you to upgrade to a different server as the "unlimited bandwidth" is actually pretty limited lol and since most of the users sites fail and never get that big they can use the term "unlimited bandwidth" for marketing reasons. In their T&C it states that it is not unlimited.
http://www.hostgator.com/dedicated.shtml is dedicated servers offered by hostgator but there is tons of other sites out there too
Pm me if you have any other questions.