Hydrogen is normally produced in a nuclear reactor by radiolysis of the cooling water. Reactors have recombiners, igniters, and other means to dispose of this hydrogen before it becomes an explosion hazard. But when the core gets too hot, the zirconium cladding around the fuel will react with the water to produce much more hydrogen. (This reaction is rapid and exothermic, so in laymen's terms this is sometimes described as "burning" the core.) In unit 1, the amount of hydrogen overwhelmed the capacity of the recombiners, accumulated in secondary containment, and exploded.
I have not had time to research the causes of the explosions in units 2 and 3.
