To sashay is to walk with an exaggerated flounce. Fashion models sometimes sashay down the runway.
When you sashay, you're showing off — but in a deliberately casual way. Kids playing dress up might sashay, and the most popular middle school students might sashay into class on the first day. You can also use sashay to describe a dance step, both a sideways square dance move and a ballet step; it's a mispronunciation of the French ballet term chassé, "gliding step," or literally, "to chase," since one foot "chases" the other.