So, from what I've been able to gather, the former president of Honduras tried to remove the term limits on his presidency via a plebiscite calling for a new consitution, which is explicitly condemned by the present Honduran constitution. In other words, the Honduran constitution has specific protections in place in order to avoid the kind of shennanigans people like Hugo Chavez and Evo Morales have got up to in their countries.
The former president persists in his unconstitutional behavior and has to be removed.
The military gets involved, but immediately the next person their constitution says should be president is sworn in as president.
Meanwhile it appears most, Obama included, have condemned the action as a coup and have insisted that the former president is the legitimate president. I suppose this only makes sense considering Obama doesn't care enough about the U.S. Constitution to present a birth certificate proving his eligibility for office. In addition, Obama is young enough to be considering similar action, though here in the States, introducing an amendment to make him El Presidente for Life isn't actually unconstitutional.
Meanwhile Chavez is so offended that someone following his example got thwarted that he's promising to interefere. While things aren't perfect in Honduras, I do think it's a sad state of affairs that we have, as of yet not seen any international support for a government that actually attempted to follow it's own consititution.