How does a suction cup hold onto a surface?

Science, baby!!!

Because when you push it agains the window, it pushes some of the air out along the edge. Then you release it returning the volume close to that of what is was originally and reducing the pressure in the suction cup. The greater pressure in the atmosphere pushes the suction cup to the window with enough force to make friction on the edges of the keep it from sliding around and to keep it against the window.

Suction cups wont work in space because there's no atmosphere.