I'm new to the jet boat world, so I'm looking at the end of the exhaust header and there is some blades in there, it looks like a propeller, my question is what is the reason for having this in there, and if I take it out is it going to affect the way the engine runs?

What you are seeing is a ballfe/muffler. It will be held in with one bolt that you will see on the outside of the header. If you are in California like me, and boat on the lakes out here you will have to have these on otherwise the popo will hassle you.  If you remove them, depending on your motor and hp it can either help or hinder performance. With my last motor, the boat actually ran better with the baffles in than out.Not sure how this new one will do

I'm new to the jet boat world, so I'm looking at the end of the exhaust header and there is some blades in there, it looks like a propeller, my question is what is the reason for having this in there, and if I take it out is it going to affect the way the engine runs?

judging from this pic u posted u have headers and its just a slip in muffler.