User blog comment:Kogath/Monster Hunter: World Discussion/@comment-6050823-20170614153734/@comment-31551221-20170615093443

I'm guessing those "fins" function similarly to the fins of the Dimetrodon or the Spinosaurus. It's a way to cool themselves. Maybe, when it's too hot, it'll spreaad them around.

This could also function like the back-feathers of a peacock and the  frill of the frilled lizard. It can perhaps also function as a way to attract females (if the Anjanath we see are males, that is) and a way to intimidate other monsters.

The frilled lizard's frills function in such a way that it makes it look bigger than it really is. This could also be the same for Anjanath because those fins make him look a lot bigger, but also they do look quite similar to wings and could make him look like a wyvern/elder dragon to others.