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.
As a final closing post, here are further links of interest relating to VR's passing:
Goonfleet held a "candlelight vigil" memorial ceremony for Vile Rat, in which they fired cynosural fields (ship-launched jump portals) as a send-off:
(at about 13:40 he shows the EVE starmap and the graphical effect of lighting that many cynosural fields in a single spot - http://i.imgur.com/TyNDi.jpg . There's also a little guitar solo and 10 minutes of silence, and at the end they start blowing each other up in remembrance of VR.)
Hmm, that does sound like a very hard problem. How would a diplomat achieve that? I'd imagine I'd be pretty angry if a bunch of drunken dicks destroyed things that had taken me months to build, so I can't imagine what someone could say to make me not want to nuke a ship.
Is it the standard "let's be level-headed about this and see what they have to say for themselves when they log on"? Or does the diplomat do something else in that case?
I played on VR's "corps diplomatique" for a while, and I can attest to it being a difficult problem.
In that situation, you have several tools at your disposal. If you are friendly with the corp (they are in your alliance, or allied in some way), you can offer repayment or replacement of the object. You can promise punishment of the perpetrator. You can allow the other corp to seek out revenge on the perpetrator (although this can escalate quickly and be bad). You can say "Tough shit, be quiet or we boot you from the alliance".
If it happened to a neutral corp/alliance, you can use the weight of Goonfleet as leverage. Goonfleet is huge, with a lot of friends, so not many people want to start a war.
Diplomacy is essentially the same in EVE as it is in real life. EVE has a huge metagame element, where various corporations (guilds) and alliances are always making deals and breaking them. I wasn't playing EVE when this happened, but Vile Rat was instrumental in getting allies for Goonswarm during their early years, which enabled them to take down one of the largest EVE superpowers. That has hugely influenced EVE's political landscape. He also served on the CSM, a real world committee of EVE players that works with CCP to improve the game as well as act as an intermediate between the players and CCP.
I hope and trust that members of CSM have no delusions that they need to be honest and fair when dealing with CCP, and Residents main focused on their goal of ripping off other players for fun and profit.