In the short term it has the same benefits as learning to do anything else that's non-trivial (grappling with a new topic, concentrating for longer periods of time, improved self confidence maybe, etc). In other words, the reasons that an elementary school would teach students to play chess.

In the longer term, there is evidence of many strong players in history who obsessed over chess and went insane. You can train your brain to do many things, whether it's memorizing 100,000 digits of pi, or becoming one of the best players in the world at a FPS video game by playing 12 hours a day, but it can't be good for your mental health.

At least for me, it's more than anything a lot of fun.

Honestly I don't care if it improves quatitative aspects of my thinking. There are other ways to do that.

But there are a couple of lessons that it keeps reminding me: to be very careful in the order I do things and to keep the ego out when analyzing a situation. Of course, YMMV.

To become good at chess you need to become good at concentration. That helps in other areas. But there's no specific reason that chess is a good way to train it, it's just a way.