What is Mining? The short answer: Miners perform computations that enable Bitcoin to be a decentralized currency system that does not rely on a master node or other authority.
The long answer is on the Bitcoin wiki.The incentive to the miner comes in the form of issuance of a small amount of digital currency. That currency received by the miner can be used to make purchases or it can be exchanged for other funds through an exchange.
As far as using a dedicated server … you may wish to reconsider. Unless it has a GPU you will be wasting your time and electricity.