The term Dedicated Servers comes from the Information Technology sector of engineering.
A Dedicated Server is usually a single computer system which is set up to perform one specific type of task within the computing environment where it resides.
There are Mail Servers, Data base servers, Web Servers and others. These servers are usually running a higher level operating system like Linux, Unix and it is tuned specifically for the task assigned to it. This is done so that all the computing power of that particular machine is directed to a specific task.
I have heard that the Google corporation has thousands of dedicated servers all running specific tasks.