As per the size of the Kaiju, they seemed like they could be monsters from Earth, but in the movie they showed that they may be alien too. So I just want to know, what exactly are these Kaijus?
The Kaiju are a race of amphibious creatures genetically engineered by the Precursors, a sentient race from the Anteverse. In 2013, the Precursors opened a portal between dimensions at the bottom of the Pacific Ocean, allowing the Kaiju to enter Earth's dimension. (Source:pacificrim.wikia.com)
So its clear from that, Kaiju are the monster created by Alien scientists.