What do they mean by season wheel in Mahjong Garden HD?

You have to match 1 pair of each of the 4 seasons. When that happens you get a bonus added to your score and the wheel in the lower right hand corner spins. Then you start over and of it with the 2nd set of each of the 4 seasons, if you want to earn 2 per game.

Or do the easy trick. Find a game where the seasons are on top. Match the 4 sets, watch the wheel spin, and hit new game…BUT hit reset puzzle so you can just redo what you did, 5 times. That’s the fast way to earn the badge.

thanks for the help .. i used your suggestion and  worked like a charm i got the badge 

You’re very welcome!