Why does a can collapse when a vacuum pump removes air from it?

Objects maintain their shape by achieving equilibrium between forces. The air inside a can exerts pressure against the interior surface that pushes the walls of the can outward, and the air outside of the can exerts pressure that pushes the sides inward.

Evacuating most of the air from inside a can removes the outward-pushing pressure, which leaves only the crushing force of the air outside to act on the can. Without something inside to balance this force, the pressure of the outside air overcomes the structural integrity of the metal can and collapses its walls. The result is a crushed can.