What you see is the redness and swelling go away. When you have an acne, the body sends more blood to attempt to fight it with white blood cells. The more blood that is sent there is the cause for the redness and swelling. When you apply ice to the area, you are causing the blood to leave that area which causes the redness and the swelling to disappear. For future reference, when you have an injury - for example, a muscle strain, you add heat to it because you want the blood to come help it treat it. When you have an injury that is swelling, like a torn ligament or sprained ankle, all the blood went to it, you add ice, blood goes away. If you want the acne to “pop” or to come to the surface, people use heat to force it to come to a head sooner.
Placing ice cubes directly on the acne isn’t recommended. Ice can stick to skin and cause a cold burn, which can aggravate acne. Instead of placing ice cubes right on top of the acne, create a compress and let the ice melt.