So, the world ends because a virus turns everyone into "fast zombie monsters" and Will Smith's character is the only survivor (until the start of the movie). It's a been a few years since the virus outbreak and he's spent that entire time has been researching a way to cure the virus (with his trusty dog).

Anyway, in the original ending the monsters attack Will Smith in his lab and in the end, he blows himself, and a bunch of the monsters, up with a grenade in order to save "the cure".

In the alternate ending, the monsters still attack WIll Smith but stop attacking at the last minute. In that moment the "head monster" points to a monster test subject he has tied down in his lab and that's when Will Smith realizes what's going on. The monsters are attacking him because he's been kidnapping "the monsters" and experimenting on them, thinking their just mindless zombies. So then the "head monster" rescues the other one and they all leave Will Smith alone.