Antihydrogen and hydrogen matter

When one atom of each comes together they annihilate each other with an explosion? What is expelled? Wouldnt they simply vanish?

A collision between matter and antimatter results in the annihilation of the matter particles. However, energy is produced instead, usually in the form of gamma rays. Evidence for this is the observed gamma emission after positron emission occurs. The positron encounters an electron (its antiparticle) and annihilates both in the collision, emitting to gamma ray photons. Therefore, two matter particles are converted into two energy particles.

So no, there is no real "vanishing", since the number of particles is conserved. Only their natures change.

Also, the reverse reaction has been observed. Photons have been observed to split into electron and positron pairs, usually after encountering other photons or matter. This observation shows that the reaction is reversible, which cannot be the case if anything vanishes completely.

When they come together, they disappear and produce energy typically in the form of gamma rays.

Some theories (Feynman) state that an antihydrogen is a hydrogen atom moving backwards in time, so both atoms are actually the same atom all along. When they collide, it's really just one atom taking a "u-turn" in time.