To elaborate on Fede_V's comment, Deep Neural Networks seem to work well on classification problems because they can automatically build abstract features from a dataset and combine them in different ways. Like, in image data they will automatically identify common shapes and patterns of light and dark, and combine these simple patterns together to identify faces or whatever (like by saying a face is a circle with two dots for eyes and a line for a mouth). Random Forests, on the other hand, are really good at classifying things if you give them meaningful dataset features to learn on, but aren't as good at building these features in the first place. By combining them together, they get a system with the classification abilities of random forests and the automated feature discovery of deep neural nets, and it seems to work a bit better than either.