In learning about how cofactors are essential to proper enzyme function, my textbook mentioned catalase and its relation to the human body. According to my textbook, catalase is similar to hemoglobin in that it has 4 hemes which cradle an Fe (iron) atom; the iron atom is used to neutralize free radicals when it "pulls on the substrate's electrons, which brings on the transition state" after catalase is holding a substrate in its active site. I already know that free radicals have one or more unpaired electrons which make them dangerous as they "seek out" an electron to complete its pair on any molecule, atom, or ion it can find, perhaps causing significant tissue damage in the process. I also know that the transition state is a key point in a reaction in which the activation energy required has been met and the reaction will continue spontaneously until it ends.
My question is, what exactly is happening here that helps to neutralize a free radical, and what is the part after the transition state doing?
If I had to guess, based on that cofactors generally can be affected during a reaction, perhaps Iron somehow binds with the free radical and share its electrons, effectively neutralizing the unpaired electron as well as using up the Iron atom? I imagine the "pulling" in the book could fit a description of a weak chemical bond/attraction, but I'm still unsure.