The Generative Adversarial Network (GAN) is a method to train and optimize AI-algorithms. A GAN consists of two components, the "generator" and the "discriminator". Let's take the example of an AI-algorithm that generates images; in this scenario the "generator" tries to produce pictures in the painting style of Picasso, for example. The "discriminator" evaluates these results and rejects them - or accepts them. A feedback loop for training purposes is established.
Only recently sites went viral that generated fake portraits, that is: computer-generated portraits that look amazingly real. But these people do not exist, compare: ThisPersonDoesNotExist.com. This is the method of the "Generative Adversarial Networks".