After watching Brave, one think that wonder me was the curly hair of the main character Merida. It’s so long! It bounces and how did it possible to animate that hair by every frame?
There are automatic hair generation and physics-based animation bolt-ons available for most common commercial CGI creation/rendering packages, these have been around for a long while really.
That said Pixar do tend to write their own software and will probably have done so for 'Brave'.
Essentially you define the area on the head where hair is to be, you can then define length, colour, drop-off areas etc. and the hair itself is then procedurally created. It's then down to the physics package to handle how it moves when moving/turning etc. and the rendered is told the reflection/refraction expected of the hair so just gets on with the job.
It's a lot of complex calculations but it's far from 'rocket science' these days, realistic shadows and flickering light are much more challenging.