With a dedicated server, you have the entire web server for your own use. Faster performance is pretty much guaranteed.
Virtual Private Servers (VPS) or Cloud Servers enable you to scale resource as and when you need it rather than being restricted by the limitations of a physical server. They draw from a pool of processing power, memory and storage depending on your requirement.
Finally collocated hosting enables you to purchase your own server and, while it will be kept in the vendor's data centre, you'll have complete control over it so you can install anything you need onto it.