You may be surprised to learn that soap bubbles can't really fly — they float! A bubble and the air trapped inside of it are both very light. In order to float, the bubble hitches a ride on a gas that is slightly denser than the air trapped inside of it: carbon dioxide!
All objects — solids, liquids and gases — are made of molecules. Density refers to how tightly packed the molecules of an object are. If the molecules of an object are very tightly packed, it has a high density. If molecules have more room to move around, the object has a lower density.
Because the air trapped inside a bubble is less dense than the air outside the bubble, it's up, up and away! The heavier carbon dioxide in the air around the bubble pushes up on the air trapped inside the bubble and off it goes.