This was covered within the arc itself. Azazel first crossed over to Earth when Margali, Nightcrawler's adoptive mother(coincidence?) experemented with magic for the first time. Since then only he could cross over to Earth and only with her help who then became his main bit$h. He then began to breed with women that would give him mutant children who then all together could open a portal large enough to cross over his who mutant army/kingdom. He wanted to take back the Earth he ruled before he was banished by the Angel-like mutant sub-species.