For many years, it was believed that neural networks (using a concept known as hidden layers) only needed a single hidden layer to solve any problem. With the increase of computing power, decrease of computing hardware cost, and advances of neural network algorithms, it's common to have hundreds or even thousands of hidden layers in your network. The increase in the number of hidden layers, among other things, is what deep learning is in a very small nutshell! Here's a visual comparison that might help in making things clearer:

As you can see in the following representational image there are several  hidden layers in the network.