Deep Neural networks have shown superior performance for learning complex abstract representations of data. These representations often correlate with our own understanding of the world. For example, a convolutional neural network learns about very high level concepts like cars, animals etc. It is even more interesting to note that it does it in a simple to complex heirarchical order. So the first layer learns simpler concepts such as edges, and then these edges are used as features to learn shapes, and so on.
It must be noted that this immense power of Deep Neural Networks can be extended beyond images. Deep learning is currently the state of the art in almost all tasks in natural language processing tasks such as sentiment analysis.