A cusp is the pointed edge where two curves meet, like the sharp tip of a crescent moon or the pointed end of a tooth. If you run your tongue along your canine teeth (the pointy ones near the front), you'll feel their cusps. The crescent moon has two cusps, one pointing up and one pointing down.

The word also describes being right at the edge or beginning of something important. When you're on the cusp of your birthday, it's almost here but hasn't arrived yet. A scientist might be on the cusp of a major discovery, having done all the hard work and now waiting for the final breakthrough. A graduating student stands on the cusp of adulthood, in that exciting, nervous space between childhood and grown-up life.

This second meaning captures that feeling of being right at the boundary, where you can almost see what's coming next but haven't quite gotten there yet. It's like standing at the very edge of a diving board, toes curled over the end, ready to jump.