So, you can basically think of eve as a giant sandbox full of stars and spaceships. There is one game world, out side of china, and the Company that runs the game, CCP, lets the player play however they want. As a result, the game encourages underhand and terrible behavior by everyone in it.
Think of the whole thing as a pirate movie. Essentially betrayal and back stabbing are encouraged, expected, and generally considered to be inevitable.
In this sort of environment, you need some one who can get other groups to play nice with you. It is a fantastically difficult problem. You have a large group of players who are actively seeking to make a profit on other players misfortunes.
Now, its 3 am on a Tuesday, and a few of my guys get drunk and decide its a good idea to go out and blow some stuff up. They get excited and "accidentally" kill a friendly ship or half a dozen. Someone has to be around to make sure that this doesn't rapidly escalate out of control, pirate bar fight style.
Add to this the fact that the "friendly" assets in question can take literally months to produce in game and are simply lost with no recourse. This is to say when you die my guys took all the stuff you had on you and you restart with nothing you had on you. Suddenly, I need to have a point of contact to ensure that 3 drunk guys don't cause a huge war with my friends between now and when I log in at 6pm tonight.
This can, as usual, include major loss of assets for everyone in my group. This translates rapidly into actual US dollar losses in some cases.
That is what your diplomats do. Make sure that when I log in after work. That the whole galaxy is NOT trying to kill me. It is fantastically hard to do. I am obviously glossing over a large chunk about in game minutiae here.