Different form of exhaust pipe...

All of the above. When an internal combustion engine enters the exhaust stroke, there's a nice little bundle of pressure and gases from that previous massive explosion that needs to go somewhere.

The role exhaust plays is taking advantage of that little bundle of pressure and making sure that it is expelled efficiently but also utilized in a way to maximize engine performance. Exhaust pressure plays a role in how the engine will handle the next intake stroke (air in, air out). It also plays a role in how the bike sounds, obviously. An engine will run without an exhaust, just not very good.

How that little bundle of pressure is routed out of the motor has everything to do with why you see so many different exhaust header and muffler designs.

Honda does the dual muffler simply to balance the bike. Their theory is having a heavy muffler on one side of the bike offsets it's balance.

That's about the simplest explanation I can offer anyway. There's way more science involved. There's just something about exhaust systems that makes the very sexy though.