To "sway" means to move back and forth slowly. Here are some examples of "swaying":

• When a couple is dancing together to a slow song, they sway back and forth.
• In a large earthquake, buildings may sway.
• Grass, trees, leaves, etc. sway when the wind blows.

Something that's hanging down doesn't "sway", though; it "swings":

Even after the earthquake stopped, the chandelier kept swinging for several minutes.

You may notice that the word "sway" is often followed by the words "back and forth".

"Sway" is also often followed by "in the wind" or "in the breeze". The word "breeze" means "wind" but sounds very soft and gentle. So if you describe something as "swaying in the breeze", it sounds beautiful and relaxing.