Neural Networks are really good at identifying patterns in data. As a classic example, if you wanted to predict housing prices, you could build a data set that maps features about houses (square feet, location, proximity to Caltrain, etc) onto their actual price, and then train a network to recognize the complex relationship between features and pricing. Training happens by feeding the network features, letting it make a guess about the price, and then correcting the guess (backpropagation).

Convolutional Neural Networks work similarly, but with images. Instead of giving a CNN discrete features, you'll usually just use the pixels of the image itself. Through a series of layers, the CNN is able to build features itself (traditionally things like edges, corners) and learn patterns in image data. For example, a CNN might be trained on a dataset that maps images onto labels, and learn how to label new images on its own.

This video uses Generative Adversarial Networks (GANs) to actually generate new images. In this case, you have two networks "competing" against each other. One network is a traditional CNN trying to identify is an image is "real" or computer generated, and the second network tries to generate new images to trick the first network.

We've been able to generative fairly realistic small images before (usually 64x64), but doing it this well on high-resolution (1024x1024) images is unprecedented.

http://kvfrans.com/generative-adversial-networks-explained/