Depending on where you go to school, I think student government actually does have responsibilities with planning events and such, and this gets far more important in college than in k12.

In k12, while it's not really meaningful, It's still an extracurricular activity, and at the same time it shows that you can work with others (theoretically) and that people like you enough to put you there.

Unless you're in an anime. The student council in anime not only has power in the school, but outside political and military power besides.