I've always loved magic tricks and stagecraft. The great thing is that even when I know what to look for, I still get drawn in by the illusionist and wind up utterly fooled. From a neurobiological perspective the key issue in most magic tricks is sensory attention. The magician draws your attention to one action in order to facilitate a ploy elsewhere.
At any given moment we are only attending to a small subset of the stream of sensory information that's pouring into our brains. Example: how does your underwear feel on your skin right now? Probably, you weren't attending to that particular stimulus until I mentioned it (or, you're cruising the web in your birthday suit).
This video, from a group (and accompanying book) called Quirkology, is a particularly nice demonstration of attentional processes.
Cool, eh? So, what's the brain substrate of attention? This is an active and vibrant area of research. A complete answer is not yet at hand, but it seems like, at least in some cases, it has to do with the synchrony of neuronal firing. In some brain sensory areas, in not so much that the average activity of a large population of neurons goes up when attending to a particular sensation. Rather, the average activity remains nearly the same but the individual neurons in the sensory area tend to fire together. Then what drives this synchrony? Information flowing from other brain regions? The release of neuromodulators that entrain synchrony? These questions are likely to yield to investigation in the not-too-distant future.