Dedicated servers are basically computers that have a single function: to host and run the websites you place on them. Unlike shared web hosting where you have to share your disk space, CPU, RAM and other resources with other customers, a dedicated server allows you to host 1 or more of your sites on the machine by yourself. The entire box is basically yours to configure as you see fit.

Dedicated servers are usually either managed or unmanaged. If you go with an unmanaged dedicated server, you usually get to pay a cheaper price, but you have to basically administer the machine by yourself. If there are security fixes for the web server or the operating system on the computer, you will need to apply them yourself. In fact, you will probably need to stay on top of such developments by subscribing to the necessary mailing lists and whatnot for security fixes to the software on your server. You are normally given the root (adminstrator) password to an unmanaged dedicated server. If you require the web host to do anything to your server, you typically have to pay extra for the support service.

Managed dedicated servers are servers where the web host attends to all the necessary updates to your software and maintains the hardware on your behalf. The charges for managed servers are usually higher since you are also paying for the services they provide. Very often, managed servers do not come with root access.