Basically, the away team (including Wesley) beam down to a planet where everyone jogs everywhere they go and they all wear strips of cheesecloth wrapped strategically around their extra-fit bodies.
These people, called the Edo, are remarkably touchey-feeley and everyone (even Worf) is having a great time.
Somehow, while every other person on this planet is getting all kissy-faced, Wesley and a BUNCH OF OTHER TEENAGERS WHO APPARENTLY ARENT HORMONAL AT ALL take turns showing off their cart-wheel skills. Everything looks pretty great and Picard is just about to approve the planet for shore leave when Wesley falls in some flowers and screws it all up for everybody by suddenly and inexplicably being CONDEMNED TO DEATH.
I guess this episode really got to me when I was thirteen because I was exactly the kind of kid who, instead of making out under the bleachers (or whatever kids did--my entire education on this subject comes from 80's movies) I was more likely to be practicing my cartwheels and falling into flowers. Except I couldn't even do a cartwheel and still can't. So, mostly, I would just be falling into flowers. And then getting condemned to death for being such a ridiculous teenager.