I saw this about a month and a half back, and from what I can gather, the Matrix is made up from machines, using artificial intelligence to take over the world. The hardware aspect of the film (based in reality.. perhaps) are all the giant octapus robot things you see flying around in the underground (I guess), and the way the characters in the film battle against these is mainly on a mental level (the software aspect) (by plugging into the Matrix), which is where all the weird surreal stuff takes place in the film. I guess these machines have supposedly taken over by making humans think everything is normal, and nothing happened, but some humans discovered there's something going on under the surface, and everything around them isn't actually real
The way the film ends (I'll give a bit of the ending away here)... when wotsisname (the main hero) Jonny Depp - when he stops the giant octopus creatures in their tracks and destroys them, it isn't known whether that happened in reality, or if this was also in the Matrix too, which takes things into another dimension, because we're left wondering what was real and what was mental/ software
So I'd guess the task of the 3rd film will be to explain what's real and what's not, and either leave us all knowing this, or leave us to go out by the DVDs and figure it out for ourselves by watching it a few hundred times