The first nuclear weapons of the type dropped on Japan at the end of World War II were based on the process of fission, releasing energy from large atoms of uranium. Fusion is the opposite process, and the one which provides the energy of our sun. It creates larger molecules, a process which also releases energy. The hydrogen bomb, or "H-Bomb," uses an atomic bomb to unleash this force, and is massively more powerful. Where uranium bombs would reach into several kilotons equivalent of TNT, hydrogen bombs can reach megatons.
The proposal to design the hydrogen bomb came from Edward Teller primarily, against the opposition of J. Robert Oppenheimer. Oppenheimer`s opposition eventually led to suspicions that he was disloyal and he ultimately lost his security clearance.
No hydrogen bomb has ever been deployed in combat.