The most amazing property in my opinion is the fact that it trains itself. (Whereas neural networks are trained by external systems).

I suspect it's related to imprinting. To take the example of filial imprinting, the brain must have some hardcoded notion of what a parent looks like. Then this is used to to build a parent detector, and the hardcoded notion is thereafter discarded. Then the newly learnt parent detector is used in reinforcement learning (near parent = good). Keep in mind that this all happens just after birth or hatching, before the visual centres of the brain have had any chance to train.

Really cool stuff.