Press space to move the points randomly once. Hold down R to keep moving them randomly. Green flag resets them. You can also drag the points around individually.
The points of a 3 dimensional cube all go to exactly three other points, one in each dimension: X, Y, and Z. This is a representation of a 3D cube on your 2D screen. Even if you move the points around, it's still a 3D cube in a mathematical sense. The red lines go along the X dimension, the green lines along the Y dimension, and the blue lines along the Z dimension.