The Hydrogen bomb works on a physical principle known as nuclear fusion. In nuclear fusion, the nuclei of atoms join together, or fuse to form a heavier nucleus. This happens only under very hot conditions. The explosion of an atomic bomb attached to a hydrogen bomb provides the heat to start the fusion.Hydrogen nuclei fuse to form helium and as this happens, huge amounts of energy are released from the hydrogen nuclei, producing a huge explosion.
Fusion releases energy due to the overall loss in mass. If you add up the masses of the particles which go into a fusion reaction, and you add up the masses of the particles which come out, there is frequently a difference. According to Einstein's famous law relating energy and mass, the "mass difference" can take the form of energy.
Fusion reactions involving nuclei lighter than iron typically release energy, but fusion reactions involving nuclei heavier than iron typically absorb energy. The amount of energy released depends on the specifics of the reaction. The reaction used in the hydrogen bomb, though, produces one of the greatest changes in mass.
The hydrogen bomb is thousands of times more powerful than an atomic bomb. There have not been any hydrogen bombs used in warfare, however there have been hydrogen bomb tests. Most of these tests are done underwater due to risk of destruction. To give you an idea of how strong the H-bomb is, think about this. This atomic bomb dropped on Hiroshima, Japan which killed over 140,000 people had the power of 13 kilotons. A common hydrogen bomb has the power of up to 10 megatons. All the explosions in World War II totalled "only" 2 megatons -- 20% of the power of ONE common hydrogen bomb.
http://www.cartage.org.lb/en/themes/sciences/Physics/NuclearPhysics/Applications/NuclearWeapons/NuclearWeapons.htm