Why do Helium-filled balloons float?

Helium-filled balloons float in air in much the same way than an inner tube floats on water. That is, if you stand underwater at the bottom of a large swimming pool and you also happen to have an inflated inner tube down there at the bottom with you, when you release the inner tube, it will quickly rise to the surface of the pool. That's because both the inner tube and the volume of air it contains weigh far less than the volume of water the inflated inner tube displaces. Hence, the inner tube quickly rises to the surface of the pool and then floats on top of the water.
Likewise, when you stand outside in front of your home, you are actually standing at the bottom of a "pool" of air that is many (many!) miles deep. So, when a balloon is inflated with Helium, it displaces a volume of air equal to the balloon's inflated size. As long as the total weight of the inflated balloon plus the Helium it contains is lighter than the volume of the relatively "heavier" air that it displaces, the balloon will tend to float to the "surface" of the pool of air surrounding it in much the same way that an inner tube floats to the surface of a swimming pool. However, in this case, the top of the "pool" of air is actually the top of the Earth's atmosphere!