A while ago someone (I forget who) posted a theory that the Monster is a genie. I thought it was farfetched and a little ridiculous at the time I read it. I had visions of the Smoke Monster cracking jokes in Robin William's voice. But after thinking about the premiere, I am now sold on this idea, at least metaphorically.
Jacob is the genie's master, and the Island is its "lamp". Jacob was once an ordinary human, and his specialness comes from control of the genie. The structures built on the Island are all part of the lamp, i.e., the means of controlling the genie and keeping it from going out of control. Jacob has used the power of the genie ("wishes") to keep himself and Richard alive, to heal people, and to make changes to the timeline. Because of the genie's arrangement with Jacob and the structures in place, it has been constrained by certain rules - for example, it can't kill its master. It resents its imprisonment and that is why it went to so much effort to set up the situation where Ben would kill Jacob. This has freed it to attempt to "go home".
The Island contains pockets of matter with highly unusual electromagnetic properties. At some point, part of the energy from this matter became sentient and is what we know as the Monster. The original entity manifested as the Smoke Monster - a cloud of ferrous minerals that are controlled by electromagnetism. The cloud is full of lightning due to all of the electrical action going on. The images are also being manifested electrically.
Ancients encountered this powerful being when it was only marginally sentient. One of the ancients (possibly Jacob), discovered a means of trapping it in the chamber we saw Ben visit underneath the temple. The trap may have involved the use of some kind of special ferrous ash from the Island's volcano.
As its master, Jacob learned how to build devices that tap into the special properties of the matter. He built some means of protecting himself from it, causing it to be unable to attack him directly. The spring was built as a means of healing and the wheel was built to manipulate space and time. Vents were created to use the Monster as a security system for the temple. Later on, some of the DHARMA installations may have been built to the Monster's specifications in order to give them more fine tuned control over the energies.
The Monster performed healing on Jacob's behalf by manipulating electricity in people. It cured Rose's cancer through irradiation of cells. Locke's spinal and and Daniel's brain injuries could be healed by rewiring neural pathways. I don't think that all healing was necessarily directly due to the Monster - a byproduct of the exotic electromagnetic properties could have been accelerated healing caused by excitement of cells.
The Monster is also able to read the minds and memories by scanning the electrical impulses in their brains. It can even perform this feat on dead bodies based on electrical impressions, assuming the brain is intact. This ability is how it "judges" people, and also explains why it's able to so convincingly manifest dead people like Locke and Yemi. The mental scanning aspect of this is very similar to how Miles' ability appears to work.
It is also able to control time flashes to some degree. Specifically, I agree with the theory on the Time Travel theory page that it deliberately orchestrated the timing of the series of flashes leading up to Locke being installed as leader of the Others followed by his murder.
While it has been clearly established that many manifestations of the dead are actually the Monster, I think that a number of them are not. The charged properties of the island allow some people whose bodies are on the island to independently manifest. This is the source of the whispers, and also all of the ghosts that Hurley is able to see. I also think this explains Christian and possibly Claire. Horace's manifestation to Locke may be another example since it was much more of a classic haunting than the Monster impersonating Yemi and Locke. The outcome of leaving a body intact on the island can be fairly unpredictable, which is why the Others burn their dead.
"Special" people have brains that are sensitive to perceiving and manipulating electromagnetic anomalies. Some of them are born with these abilities, or they develop due to exposure to the Island's energy. The Island's properties make it much easier for these people to use their abilities there, but they are also able to use them off-Island. The abilities manifest a subset of the same basic powers that the Monster has. Many people have precognitive dreams and visions (Charles, Eloise, Ben, Locke, Charlie, etc). More powerful people can perceive ghosts (Hurley), project themselves (Walt), read living and dead minds (Miles), and heal (Jacob).
what the heck is going on?
Through experiments with space and time, Jacob became aware of a catastrophe pending in the future (possibly in 2007 or 2010). With awareness of the chain of events leading to the event, he has been attempting to manipulate events using the Monsters and his own abilities to avert the catastrophe. So far, he has failed. The purpose of the Others is to help Jacob attempt to fix things, and also to help act as jailers of the Monster. Jacob saw possibility of his own death, and he was responsible for setting events in motion to set off the nuke. The creation of this alternate reality is his last ditch effort to set things right. He specifically brought Hurley to the island so that he can continue to give instructions even after death.
The Monster has encountered many humans during its time on the Island. Time and time again it finds evil and corruption. It is unimpressed with humanity, and wants out of the trap Jacob has it in. It wants to get out of the lamp and go home. After killing Jacob it thinks that it is finally free, which is why it was going off on a "you're all free!" kick on the beach. Its next move will be to destroy the mechanisms that are trapping it so that it will be able to leave.
Where's home? I'm not sure yet, but I've got two theories. One is that home is another dimension or planet. The other is a little odd. Someone else had a theory that the Island was originally in Tunisia, but then something ripped it out of the ground and sent it to the opposite of the Earth, where it became an island. If that turns out to be the case, I think the Monster's home is Tunisia.