This little "game" is intended to teach you how to work with Euler angles. The idea is that you're sitting in the cockpit of some airplane and the green crosshairs show where your plane is headed as well as its orientation. (The shorter line is for the up/down direction.) You're supposed to steer it so that the green crosshairs are perfectly aligned with the red crosshairs. You can make three movements and the available movements are the rotations, called roll (x), yaw (y), and pitch (z), around the plane's three axes.
Which of these movements can be used and in which order is controlled by the order pull-down menu while the action field always shows the name of the next movement to be performed. The actual rotation is controlled with the mouse (with the mouse button pressed). Click next to indicate that you're done with one rotation and want to perform the next. Click reset to start anew and click shuffle for a random repositioning of the target crosshairs. The main challenge is one of the so-called "proper" Euler angle sequences where one of the three rotations is not available. Try for example YZY, i.e. yaw-pitch-yaw.
The world around your "plane" is rendered as if you were inside of a sphere looking at one of its poles initially. But you can switch this off if you feel distracted by it.