Here is a detailed reddit post, explaining (roughly) what exactly is going on in the picture above,
In terms of money, the bigger ships, like the titans in the picture above, are generally sponsored, so its cost is usually split between either the coalition or organizations.. However I'm sure many people pay face value.
Though I was not personally involved in this particular engagement (thank god), I play EVE and I am actually a member of one of the coalitions pictured here (Clusterfuck Coalition, or CFC). What you see here is a combination of small ships (too small to matter, in this case), Dominix-class battleships, which serve as drone platforms, as well as a mix of carriers, dreadnoughts, and titans. I can't seem to spot any supercarriers, but I would not be surprised if they were involved.
I'll try to explain this as best I can. In EVE, combat happens on "grids," which are usually around 300km across, but can be longer depending on the size of the action. This one was likely much longer. Ships can travel at sub-warp speeds (almost always under 4km/s, generally <500m/s for most of the ships you see here), or they can warp away at very high speeds. Normally, to escape an engagement, a ship attempts to warp or jump away; jumping is a little different, but also can serve as a method of escape. Those huge blue bubbles you see here are interdiction spheres; ships inside those spheres cannot warp or jump to escape. These spheres are also very very large, and since the max sub-warp speed of many of the ships on the field is below 500m/s, their only method of escape is to "slow-boat" out of the bubbles, which takes too long to be considered a viable option for most of the ships seen.
I'll skip past most of the ships, but you'll notice in the center a blob of large, mushroom-shaped ships, and a few other blobby ships roughly the same size. These are called Titans, and they are the largest, most expensive ships in EVE. By my calculations, each of these is worth ~$3,333. That giant yellow death beam you see there is called a Doomsday, which is the most powerful weapon in EVE. It costs fuel to fire, and can only be fit to/fired from a Titan. It is so powerful that one shot can destroy some capital ships, including carriers and dreadnoughts, as seen here.
Now I'll explain why this fight was absolute hell. In EVE, when a node on the server is under a great deal of stress, the server activates "time dilation." This means for each player, the game continues running at full FPS, but the server itself runs more slowly. For example, at 10% TiDi, the game runs 1/10 of its normal speed, meaning each second in game takes 10 seconds to be processed. The Dominix class battleships I mentioned earlier serve as drone platforms, and each of the (hundreds) of them involved spewed out 5 drones. This massive number of entities, combined with each of their damage figures and the other ships being fielded, caused huge time dilation to occur. It got to the point where players jumped into the system and it took over an hour for them to load, during which players who had already loaded could open fire on them.
The end result was a battle that took likely less than an hour of game time, but was stretched out to several hours of real time, with many players getting killed before they had even loaded in. This also sheds some light on why EVE is sometimes more fun to read about than to play: though this fight looks cool, and the power struggle between the two coalitions makes great reading material, in reality the players involved in the fight were likely not paying attention to the game at all. The time dilation becomes so huge in fights like this that it's not uncommon for one to load on grid (if they're lucky), activate their attack modules on the primary target, and then do something else, whether it be reddit, making some food, cleaning their house, or some other menial task that ends up being infinitely more entertaining than watching a spaceship float by at 1/50th of its normal speed.
tl;dr Because of the number of ships involved, the server slowed time down during the fight, meaning it was extremely boring for those involved. If you want more details, read the fucking post, I worked hard on this.
EDIT: Fellow Gaffer Pulsemyne was there, and had this to say,
I was there-ish. At the peak there was a little over 4000 people in the system, about 50+ titans, over 150 super capitals and possibly nearly 1000 capital ships. There was also hundreds upon hundreds of Dominix ships (battleships), Ishtars (Heavy assault class), Stealth bombers and intercepters. Oh and Dictors (they make the bubbles you see on the OP's picture).
This was a battle between my lot (The CFC, Clusterfuck Coalition) along with russian alliances; against the forces of N3 and Pandemic legion. Lately N3 has been using massive amounts of capital ships (in particular the archon carrier) as a sort of unbeatable blob. They deploy thousands of drones and wipe everyone out. It is proving to be a very effective tactic.
One of other benefits of this tactic is that it causes a bum load of TiDi, or at lest it does when you try to fight their blob with another blob. Whoever is on the field of battle first has a big advantage and yesterday N3 were ready and waiting.
Our forces were up for the fight and decided to jump into the system and duke it out. We cyno in a buttock load of Dreadnaughts ready to try and kill the carriers and then...TiDi hits, big time. The titans start killing the dreads with ease as people find themselves unable to do much. Lot's of pilots report their modules not working while some even find themselves dead before the system has even loaded. By the end of it hundreds of dreads are dead with little to no real loses on the N3 side.
At the moment the game really cannot support the kind of battles the super alliances want to have. We all play the game in order to just have some fun and kill spaceships. Whatever side you were on yesterday was little fun if any. TiDi maybe better than lag but it's really bloody boring to watch a spaceship battle in super slow motion.
While N3 won yesterdays battle it's a fact that both sides are so big that neither really wants to tackle each other head on. At the moment it's a proxy war of sorts. No one is really in the mood to grind soverighnty endlessly.
So it was basically a big fight over...nothing.