If a cork is held below the surface of water and then released it rises. The density of cork is less than that of water, so the weight of water displaced is greater than that of the cork itself. In accordance with Archimedes‘ principle, the cork is acted upon by a resultant upward force equal to the difference between its own weight and the weight of the water it displaces.
A hydrogen-filled balloon rises in air for precisely the same reason that the cork rises in water. The density of air is about 14 times that of hydrogen. The total weight of a balloon consisting of fabric and hydrogen is thus much less than the weight of air it displaces. The difference between the two represents the useful lifting power of the balloon.