The pirates are fighting for money. Specifically, personal profit.

This is not due to a lack of things to fight for in the area. They could fight against the Islamic fanatics that will probably kill them and their families eventually. They could fight against the corrupt attempts at government. They could fight against assorted invaders or drug smugglers or evil warlords. But rather than any of those things, they fight unarmed sailors to hold them for ransom.

Oddly enough, the main beneficiaries are tuna. Tuna are in danger of being wiped out by massive factory fishing. But the fishing ships are steering clear of a big chunk of ocean now and the tuna have what is almost a much needed de facto sanctuary.

They are after money. Somalia is a failed state. There is no real government, no security, no industry. In this situation, the some of the people are turning to the only available commercial possibility. When it's your family at stake, you will do almost anything.

They are fighting for bare survival, trying to adapt to the circumstances as best they can.

I don't know. This question is as generic and hard to answer as asking what are terrorists after. Everyone has their own agendas. Obviously for many, the purpose seems to be profit from ransoms. Perhaps others want to protect the waters from foreigners. But they don't seem to be organized. There are different gangs after different things. Some are even rumored to be funded by wealthy people in the UAE (almost like those with letters of marque back in the day!)

And of course there's also the fact that Somalia is a completely failed state without any way to enforce laws. And I think pirate gangs have replaced the state in a sense, enforcing their own rules and just organizing into something, creating their own mini pirate societies. "Pirates at first were interested in securing the waters before businessmen and militias became involved." -Wikipedia
But there isn't a central pirate authority so you can't be clear on what they're after.

From the YouTube clip, the Somalia Pirates are looking for ransom money. 30Million last year.

I find the excuse that they're making that the pirates are doing this because of illegal fishing or being a garbage dump is ridiculous. Illegally seizing commercial liners is not a way to get attention.

I don't think we should expect that all of them would fight for the same reasons. Money may be the primary reason for some but there are other ways (both legal and not) to make it. Piracy may not be as organized as we think, obviously not as organized as the "families" that do someone elses's dirty work.

Money, Money, Money. The pirates are trying to get money from the shipping companies who own the ships. Up until this weekend there hasn't been much resistance from governmental agencies. Somalia is essentially a failed state. There is no government to speak of.

First, it should be known that Somalis and the pirates do not call themselves pirates. In its beginnings (early 1990s), Somali fishermen were frustrated by foreign ships that dumped their toxic waste into Somalia's waters. These ships belonged to successful Western companies. In other areas of Somalia's coast, other countries' ships (Korean ships often did this) would overfish - without permission - in Somalia's waters. The civil war just broke out and the economy was doing very poorly. It's was and still is difficult to get a job in Somalia so many rely on what little they could do to provide for their families. So this greatly frustrated fishermen who depending on whatever they could fish to make a living.

Somalia took its case to the UN, who repeatedly ignored its claims of foreign ships taking advantage of its powerless - by polluting the waters and killing fish (and many children who went into the waters became sick after swimming) and overfishing. The UN refused to investigate the matter. So the fishermen decided to take matters into their own hands and keep out and intruders. They did not kill intruders however. In the past, they were known as Somalia's unofficial coast guards.

It was recently realized that people can make a lot of money from ransoming people who intrude in Somalia's waters. So warlords who rule the cities of the especially chaotic south of the country sent their followers to the northern coasts to kidnap and ransom intruders. It is these people who are do what pirates are known to do - rob at sea. However, even these people did not kill their victims and even made sure to have enough food and alcohol (Somalis are Muslims and so alcohol is hard to find in the country) to offer the victims, as they wanted to treat whatever would result in a large amount of money well.

However, due to propaganda of Western media (easily the most influential media in the world), the background of Somali pirates are not known and instead are said to be random thieves who ought to be controlled. No one ever seems to care to mention about the issues that resulted in this piracy and how to deal with it. Instead, it seems that Somalis are expected to just let others take advantage of their waters while they watch their waters continuously being polluted. Right now, the US Navy is stationed in Somalia's waters, killing any and all "pirates" on sight. There is no mention of whether or not foreign ships in Somalia's waters are being dealt with but something tells me that they are not.

A bullet in the head apparently.