[halfcat]

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.