This activity explores the force of air on objects. The particles of air that are all around us push in all directions--that's called air pressure. The card sticks to the rim of the cup because of the adhesive property of water, but it stays in place because of the force of the air pushing into it.
Water is incompressible, which means that you can't squash it to make room for air. When we tap the jar, the force of gravity pulls water molecules down, leaving a region of low pressure in the cup. The force of air moves from the high pressure all around us, into the region of low pressure.