What's the input to the Generator?
In the basic implementation of GANs, the Generator only takes in a vector of random variables. This might seem strange, but after training, the generator can transform this input noise into an image resembling those of the training set.
How does it work?
It is trained along with its counterpart the Discriminator, whose goal is to distinguish real images (i.e. the dataset's images) from fake ones (i.e. images produced by the Generator). The Generator's goal in training is to fool the Discriminator into thinking that its images are real.
In the beginning, where they are both untrained, they are both "terrible" at their respective tasks. The Generator can't produce anything resembling an image, but the Discriminator can't distinguish real from fake. As training progresses, the Discriminator starts identifying ways to distinguish the real images from the fake ones (i.e. patterns that appear in real images, but not in fake ones). The Generator, however, in its attempt to fool the Discriminator, starts producing those same patterns in its own images. After a while of both models becoming better at their respective tasks, we reach a point where the Generator can produce realistic images and the Discriminator is very good at distinguishing between real or fake.
Edit as suggested from comment:
A vector of random values is used as an input, so that the Generator can learn to generate unique outputs. In itself the Generator is deterministic, meaning that it has no internal sources of randomness. If we give it the same input vector twice, it will produce the same output both times. Thus, we feed the Generator with random values, so that it can learn to produce different outputs, depending on those values.