It's spongy because there is a lot of air that has been whipped into the egg whites - as long as the bubbles remain intact (which is why sponge cake recipes tell you to gently fold in the beaten egg whites with a rubber spatula and also why you should use the eggs as soon as you've beaten them), the bubbles will act as leavening and expand in the heat of the oven, thus producing an airy sponge. The presence of fat mitigates this effect, which is why cakes with more yolks in them are less spongy.

Simply put: Sponge Cake is normally made by whipping the eggs (either whole or yolks/whites; with sugar) to their full volume and then folding in the flour. It's spongy because the eggs are the leavening agent here and provide the "spongy" structure.