Using a pen/stylus for me goes back over 20 years when I owned an Apple Newton. Then I owned Palm Pilots and various other PDA's in the 90's and early 2000's.
Then Steve Jobs stood up and delivered his snarky comment about "A stylus? I have 10 of them".
Well, like other things that Jobs talked out his a$$ about, there's actually tons of reasons, awesome reasons, for using a pen/stylus. He just didn't know.
Besides taking freehand notes in meetings (hey Steve, good luck with your finger doing that), sketching design ideas is unbelievably simple, productive and fun with a pen. Also, I find navigating around the Note 5 much faster and far more accurate with a pen. This emerged over time when I found myself pulling out the pen if I knew I'd be poking around screens for a few mtinutes. It's really something you don't know you need until you get used to it. Then using your finger sort of feels like using a baseball bat (no I don't have fat fingers) when navigating around the interface.
I'd suggest that if your wondering what the pen could be used for, you should just make a habit of using it a bit, then see how well your finger works after that. I imagine everyone is different, but for me, the pen is a must.