What is the science behind a cake rising?

Self raising flour.
Self raising flour has a small amount of "baking soda" (Sodium Bicarbonate aka bicarbonate of soda) added. This combines with acidic ingredients in the cake mix to produce millions of tiny carbon dioxide bubbles, which cause the cake to "rise".

There is also a small amount of tartaric acid to ensure that it rises even if there are no acidic ingredients.