You can't really understand it without the maths/physics that you will learn if you study chemistry or physics at university. (If anyone can be said to understand it, as distinct from merely knowing the solutions to the equations. I don't claim to.) Any hand-waving explanation we try to give at this level (or indeed undergraduate level), some quantum physicist will pop up and say "that's not true". And it isn't really, it's just a model to try and help us understand. But lots of things in quantum mechanics have no analogue in classical physics, so any mental model we construct in terms of familiar things will necessarily be inadequate.

I think pauli's rule applies to only atomic orbitals.

No, it applies to MOs as well. Of course the "four quantum numbers" of an electron in an atom are not directly applicable to MOs, but the general principle still applies. Two electrons can have the same spatial wavefunction (i.e. "occupy the same orbital") only if their spins are opposite. So no more than two per orbital. This is a consequence of the fundamental properties of fermions (particles with half-integral spin); one of those things with no classical analogue.

Why do you think He

_{2} doesn't exist? If two 1s atomic orbitals, each with 2 electrons, can form one MO, to which Pauli's principle doesn't apply, why can't you get 4 electrons in a bonding MO and form a really strong bond? The answer is that Pauli does apply; the 2 AOs combine to give 2 MOs, one bonding and one antibonding, each filled with 2 electrons, so there is no overall bonding.

Another approach to the question is via symmetry. Any solution to the Schrodinger equation - any permissible electron wavefunction - must conform to the symmetry of the molecule. For H

_{2}, for example, this means, among other things, that it must be either symmetrical or antisymmetrical with respect to interchange of the H atoms. Now the individual atomic orbitals, 1s

_{A} and 1s

_{B}, do not satisfy this criterion - they transform into each other, not plus or minus themselves. However, we can form molecular orbitals that satisfy the symmetry by linear combination of the atomic orbitals; in this case (1s

_{A} + 1s

_{B}) and (1s

_{A} - 1s

_{B}). The former has lower energy than the atomic orbitals, and the latter higher, so the two electrons go into the bonding MO and form a stable bond. Note that the output of this mathematical process is always the same number of orbitals as you put in; that's how it works.

Their electrons can have only one wave, they should either be constructive or destructive and they can not be both. So then they must form only one molecular orbital, right ?

Distinguish between electrons and orbitals. Electrons are real physical things [some might dispute this statement], orbitals are not; they are mathematical abstractions, possible states that an electron might occupy. So two actual electrons in an actual molecule may interfere either constructively or destructively, but not both at the same time. But both

*possibilities* exist - that, in a sense, is what we mean by saying "the two AOs form two MOs". And spectroscopy demonstrates that electrons can and do occupy these other states (however briefly), and undergo transitions between them. So in that sense all these other orbitals are "real".

I hope all this is at least some help, not just a load of mumbo-jumbo.