Play the tutorial (button in the upper-right corner)- it only takes about 30 seconds.
Or watch this video (2:30):
Or read these words:
This game was designed to model a question in digital topology which was unsolved at the time (2014). Each level represents an abstract "digital image", and beating the level is equivalent to showing that the image is reducible by a homotopy equivalence to a smaller image. When the game launched, the original solutions for each level were stored in order to catalog which images were reducible and which were not. Here are some technical mathematical links: