Anyway, in a nutshell the theory is that monkeys and other primates have cells in their brains called 'mirror neurons'. These fire the same patterns whether the monkey performs an action, or observes another monkey perform that action. In other words the monkey is modelling the experience of the other monkey, and experiencing it as if it was his own. We all know what that feels like - when you see someone cut their hand, your hand hurts, when you see someone on telly crying, you cry too.
This links in with the other thing I believe, that primate intelligence is social intelligence, and human mind is a social distributed system.
Here is a quick overview of the theory on the livescience web zine, and here is a paper linking mirror neurons to language development, and here is a paper linking mirror neurons to the rapid evolution of the human mind.
ETA here is a cute video of a sweet little baby monkey, showing mirroring.