Re: what is deep learning?
Yes, it is sort of like a human brain - simplified in some ways and made more complex in others, obviously. The "deep" bit of "deep learning" normally refers to the fact that you have multiple layers of neurons between input and output. As you increase the number of layers you increase the potential performance of the network, but you also massively increase the difficulty of tuning the network to get that performance. In many networks you also lots of feedback loops of varying degrees of sophistication, as well as lots of different types of neuron and connections and so on.
We don't yet have a full understanding of really complex neural networks, and there's no real consensus on the "best" or "right" way of designing them. We have a lot of techniques that work fairly well, but we don't know whether they're the best way or how to prove whether they are or not. The maths and scientific understanding is quite a long way behind the empirical engineering (for now) and much of the design is trial, error, instinct and proprietary "black box" stuff (which is almost certainly 1% real progress to 99% "we did this and it worked but we don't know why so we'll keep quiet about it").
Custom hardware is therefore important for researchers because, in the absence of a really sturdy mathematical base on which to build, progress is mostly made by trial and error, and faster chips like this allow more rapid iteration. If you're really curious about this stuff there's an excellent primer over at http://neuralnetworksanddeeplearning.com/.