Sponge cakes are light and airy. The primary reason they rise so high is the air beaten into egg whites. Sponge cakes are both lighter and dryer than butter cakes. They are dryer (in a good way, not like an overbaked cake) because they don't contain the fat that adds to the moistness of butter cakes.
Butter cakes blend sugar into the fat to make the air pockets. In contrast, sponge cakes whip the eggs with sugar until light in color (lemon-colored), thick, and at the ribbon stage (when the batter forms a flat ribbon falling back upon itself when the beater is lifted). At this stage, a line drawn with your finger through the batter will remain visible for at least a couple seconds. Whisk-type beaters, not paddles, are always used to make sponge cakes. The air whipped into the egg-sugar mixture at this stage contributes to the rising of the sponge.
When the sponge cake is placed in the oven to bake, the second essential factor is the heat of the oven. The liquid in the batter becomes steam, which rises and escapes through the foam. The heat also causes the air in these bubbles to expand, which contributes to the rise of the cake. This same principle is what makes croissants flaky and puff pastry puffy.