Melee DPS means that you are right next to the enemy you are damaging. Think of it like being in a fist fight. If you are not close enough to hit the guy with your fists you can not damage him.
Ranged DPS means you can hit your enemy from a far, like a gun fight. Range does not play a factor in the amount of damage your weapons or spells do. While you can shoot the guy standing right next to you, Range DPSers have a lot less armor then meleers so you will take a lot of damage with them standing next to you.
Range have abilities to root their enemies in place, slow their forward progress and even knock them back. How ever meleers get abilities to over come those abilities, so it becomes a game of act react. A range guy can usually stand back and fire into the battle. How ever meleers will come after you to kill you. If they can catch you with your limited armor you are going to take a lot of damage. One on one meleers and ranged DPSers should be pretty even, however I would usually give the ranged a slight advantage. Most non-player mobs do not have the ability to over come the range DPSers roots, slows and knock back.
As far as who can do the most damage in a group usually ranged DPSers put out more damage in a group but if a mob breaks free you are pretty much a goner.