It is a significant part of Machine Learning. And it tries to mimic human brain in a sense. There have been many failures as well as successes.
Speech Recognition & Image Recognition are huge successes.
It is a promising subject and opportunities are growing. It can probably predict medical problems or traffic bottlenecks on the road.
Ray Curzweil [Author of “How to create a mind”] is leading the initiative at Google and likewise Microsoft is also making progress in Deep Learning.
May be, some time in future, the AI System will be able to answer that dumb question: where do you find yourself 5 years from now?
The possibilities are endless. Exciting and Scary, at the same time.
Read this long & old [I am sure it must be few years, say 2013] but very interesting Technology Paper [before Google came out with Tensor Flow] from MIT: