So you link to a site which has a GREAT BIG BUTTON saying 'find out more' which when clicked tells you all you need to know about the dedciated server options on offer, yet you say you want to know more about dedicated servers? Odd. Anyway, I've deleted the link as it appears just a little bit spammy from where I am sitting. Assuming you really want to know what a dedciated server is then how about the most basic of descriptions which pretty much sums it up: a dedciated server is one that you lease/hire in entirety and is not shraed with anyone else.
A dedicated server is a server that is dedicated to perform a certain task only all the time. For example, a dedicated web server hosts only web services (such as apache, tomcat...) and doesn't have another services such as FTP or DNS as an example.
So, let us say that you are hosting a website. One design can be:
So, if you decide to use dedicated servers for each service, then in this case you should get 4 servers and each server will be dedicated to a certain service.