Scars are fairly common. In a dangerous world such as that of a typical roleplaying game, people get into fights and other perilous situations, and may emerge with battle scars or other marks of their adventures.
A scar can simply be a cosmetic change with no game effect. Or it could make someone look uglier or more intimidating. Or it might make them look cool. You can basically pick any game effect you like and have it make sense. So they're pretty versatile, and you can use them as a physical manifestation of almost any modifier to reactions of other people.
Commentary by memnarch (who has not seen the movie)
Well then, that'd explain why Kylo's up and about with Finn still being presumably stuck in a medbay somewhere. Team Bad Guy wouldn't care about appearances if it gets a powerful minion up and moving again. Heck, if Kylo hadn't taken the helmet off, he'd still look like a knock-off of the original of "don't care, just get them not dying and moving again". I know the shapeshifter thing is just an Irregulars invention, but I'd have thought that a shapeshifter could just shift away damage like that.
And another task? One that's practically impossible without doing the other ones? At the very least, I'd think finding these ancient Ahch-To texts would be very difficult without finding Ahch-To. But maybe that's the point and I can't think of a reason why it'd work yet? Or perhaps there are some texts that were taken from Achoo that are stored elsewhere. Any one of those could possibly provide some clues on how to get there.
And treating paper as just a thing? That's how you know Snoke is a super Bad Guy. Hm, I wonder if there's meant to be something more to all of these book references for Snoke. This is like comic episode number three with that kind of reference from him isn't it?
Snoke: Let’s see what Rey did to you.
Kylo Ren: I remove my helmet, revealing a carbon fibre synthskin scar running down my face and neck.
Snoke: A good start. But if you want to be truly badass you need to get a hand chopped off.
Kylo Ren: Well that shouldn’t take long.
Snoke: There’s something else I want you to do. Maybe with more tasks you might actually complete one.
Snoke: Ahch-To is the repository of ancient Jedi texts. Find them and bring them to me.
Kylo Ren: But they’re written on paper. The Forbidden material. Are you sure you want to be playing around with those things?
Snoke: They’re just books. No harm ever came from reading a book.
Rey: <cough> Giant Sand Creatures...
Snoke: Well, maybe once.