Edit: HERE is a pretty awesome view of the beginning of the fight with comms included. Even if you don't know eve, it's well worth checking out. The flashing whiteish/red circles that keep popping in are new super capitals and capitals exiting jump portals
Essentially, there are two "Mega" coalitions in the game right now, the Cluster**** Coalition (CFC) and the Honeybadger Coalition (HBC). A coalition is a group of alliances that band together. There are also 3-4 other smaller coalitions (Russian Bloc, N3), as well as some independent notable alliances (Black Legion in this case).
These are all Nullsec powers. The HBC's core alliance is TEST; an alliance that is based from and recruits out of your favorite website, Reddit (Shameless plug: go to /r/evedreddit to check out Reddit's corporation/alliance, and clickthis for a free 21 day trial)! The CFC's core alliance is Goonswarm, which is based in and recruits out of your least favorite website, SomethingAwful!
Now, it would appear that these two alliances were born to be rivals, but it was not always this way. When the reddit corporation (alliances are composed over individual corporations) first joined EVE, they were attacked by the SA corporation, goonswarm; who were already very established in the EVE universe. Instead of becoming enemies, the Goons were taken aback by the adorableness of our attitude towards the game, and we became allies and soon to be best friends. They nurtured us, tought us, fought for us. Our current leader, Montolio, decided that he wanted to take a path of independence.
We met another group of players in an alliance called Pandemic Legion. They are considered the big bad guys of EVE. They posses hundreds of the Super Carriers and Titans; the most powerful ships in the game and which the pictures in the OP are mostly comprised of. Basically, these guys have a public mumble channel called OG mumble. Mumble is a program like teamspeak, if you didn't know. This was when Battlefield: Bad Company 2 was popular, and some of our guys joined their channel to play with them. They befriended them, and more people joined to play and more and more. Soon, their EVE alliance had invited us to go on campaign with them; and it was hella fun. They were a bunch of old players, and our raw enthusiasm of the game seemed to make it more fun for them, and their wealth, power and experience taught us a lot.
The problem is, that our new PL friends are direct enemies with our Goonswarm bros. These tensions were drawn down, and we eventually got both of them fighting for us to attack a new threat to us in the South. But that'sanother story.
What's important to last night is that we chose to go with PL instead of goons, and we formed our own coalition; the HBC. Between PL's ability to drop many of the most powerful ships in the game, and our ability to rush in with hundreds of support ships to back them up, it's a potent force.
Last night, a relatively small pirate alliance that controls a good bit of territory nearby Goon-land thought that the goons may try to attack them over a local moon; which holds mineral resources. They informed a fleet commander in Pandemic Legion that this may be happening, and PL set up to ambush goons.
The goonswarm Fleet commander (FC), Dabigredboat, is a prettty interesting character, who is loved or hated throughout the game, but that's another story. Anyways, he is flying a titan. These are the most powerful ships in the game, they do a lot of damage, can take a LOT of damage, and are ridiculously expensive. Additionally, they can move across the universe rapidly with a jump drive; but they can also move OTHER SHIPS across the universe rapidly by "bridging" them.
Sidebar: EVE has an interesting feature where people can buy game time cards (30/60 day) and sell them in game for in game money; allowing wealthy people to essentially play the game for free, and allowing people who are wealthy out of game to have the money to do what they want. This provides a rare insight to the actual value of in game item. And a titan, like dabigredboat's, would cost something like $3500 dollars to buy with out of game money.
Back to the story. So basically, boat is in his titan getting ready to bridge a full fleet (~250 dudes) onto this small pirate alliance. Except he makes a mistake; he clicks JUMP instead of BRIDGE. That sends his $3,500 ship right into the middle of this pirate corporation with nobody nearby to support him. And then all hell breaks loose.
If you'll remember, PL was aware that something might be going down, and when the pirates inform them that a titan has jumped in, and not only a titan but Dabigredboat's titan, they jump in 3-4 supercarriers. Supercarriers do more damage than a titan, but don't take quite as much and aren't quite as expensive. Boat orders Goon and CFC supers to log in, and they drop a few more supers in to help boat. PL goes into hyperdrive and goes all in; they drop every supercarrier they have available, and are frantically calling everyone they know to get there as well.
And then Boat makes a crucial mistake. He should have realized that his titan and the few supers he called in to support him were going to die, and cut his losses. But instead he panics, and calls in EVERYTHING the CFC has to help get him out of there. At this point, the battle transcends hell and goes into every god damn layer of Dante's Inferno. The CFC commits every supercarrier, titan, dreadnought (basically floating gun platforms that do a ton of damage) and regular carrier (which are basically "healers") that they can. PL does the same, and the rest of the HBC is in right behind them. My fleet, and the rest of the TEST fleet burned across the universe at best speed to get into the fight, and all of our capitals (dreads/carriers) and supercapitals jumped in ahead of us.
Also, goons are not well liked in the universe of EVE. They have fought against (and won against) pretty much every major player in the game. So the rest of the smaller coalitions also jump into the fray. And even though we're technically "unfriendly", they join ourside and the whole universe of EVE piles onto the CFC. My poor laptop crashed when there were 2800 people in the solar system (And there were hundreds more in surrounding systems), but it was epic.
The CFC lost a lot of shit. ~44 Dreads, 29 Carriers, 5 Supercarriers and 3 Titans. The HBC and the rest of EVE lost 10 Carriers, 6 Dreads, and one Supercarrier. It's a mind boggling amount of damage done, and money lost. But that's EVE.