There are 2 main categories of server based on the accounts it holds. The normal kind is a shared server which hosts many different accounts/sites belongs to different owners. All sites share the server’s resources and have various resource utilization limits set by the server admin so that no one site hogs more than its share of server. Also the owners have limited access to the server and do most of the operations via a 3rd party control panel or jailed shell access.
Dedicated server is exactly opposite of a shared server in the sense that the complete server resources are owned by a single owner. He can host as many sites he wants and set his own rules for their working. He has root access to the server and can basically do almost everything with it. Dedicated servers are offered by web hosting companies for small extra fees, which they charge for server maintenance and normal trouble shooting activities.
Dedicated servers are best if you are running critical, high database usage sites and if you have some basic server management skills.