I think he's just highly, highly intuitive, with a good grounding in human psychology and a finely-tuned understanding of what motivates people.
There's clearly no supernatural element to it - and he's said so much himself - but our brains are capable of a whole lot more than we often realise, and he's tapping into that. People like patterns, and unconsciously seek them out, and I think Derren somehow understands the patterns people are looking for and either panders to their expectations or subverts them, if that makes sense.
I'm by no means psychic, and am certainly not capable of any feats on Derren Brown's level, but I do think I'm unusually observant and sensitive to things. I've only recently come to understand this (partly by reading a great book called The Highly Sensitive Person), and it's been a bit of a mixed blessing - social situations, such as parties, can be overwhelming, as I'm processing so much information at once and always flitting between different things. My best friend - who in many ways is my polar opposite - will walk into a party, spot one person she recognises and become engrossed in a conversation. I, on the other hand, will pick up on all the different discussions, notice from their body language that the couple in the corner have had a row, identify the smell from the vase of flowers on the table, notice when the background music changes, or the noise in the room picks up/there's a lull, spot the person who is quietly sneaking outside to smoke and so on. I think Derren Brown is doing a similar thing on a very magnified level.