Deep learning is associated with artificial intelligence and mainly allied to neural networks , the goal of a neural network is to learn and recognize patterns, for this makes use of several neurons, which form a network, such as the following image .
The values of W represent the input of data in a neuron and the output of it will be connected in other neurons, each neuron has a "weight" that is called a threshold and that defines the function made by it.
Important to point out that they are unsupervised networks, they learn alone without human supervision.
Deep Learning-inspired machines can learn complex abstractions of data through a hierarchical learning process very similar to what occurs in the human brain - especially in the visual cortex.
Assoonasanetworkismountedandtheneuronsintheinnerlayersareresponsibleforidentifyingsmallpatternsinsomethinglarger,forexampleinthe"7" character check, a part of the network recognizes the angles and directions of each pixel in the image.
In its quoted case of pornography, the neural network is able to identify small patterns and that if added they can affirm that, for example, what appears in the image is a penis.
There are several neural network evaluation techniques, I think this is a bit outside the scope of your question, however I suggest reading about Perceptron / a> and Backpropagation .
Deep learning can have the input of many things, mainly unstructured data and can be used for recognition of photos, sound, videos, texts and others.
For more details on Deep Learning I suggest this post.