When you theorize, you come up with an explanation for how something happens, based on ideas that can be tested. You may theorize that your dog is afraid of loud noises after you see her cower under the bed during fireworks and thunderstorms.
When someone theorizes, they're not just making a wild guess. They're forming a theory, or a testable explanation that they can confirm through experimentation. After a scientist theorizes and the theory sticks around and is tested again and again in a rigorous way, it becomes an "established theory," like the theory of gravity or plate tectonics theory. The Greek root theorein means "to consider, speculate, or look at."