Something that moves easily back and forth, like a swing.
The word 'swingy' makes people think of fun, play, and being carefree.
Examples:
The swingy door moves when you push it.
Her dress is very swingy when she dances.
The swingy branches move in the wind.
I like my swingy chair because it's fun to sit in.
The swingy bridge goes up and down a lot.
The swingy music made everyone want to dance.