To rush is to hurry or move very quickly, like when you rush to get to class on time or rush to catch the subway instead of waiting for the next one.
Rush implies urgency — you need to get somewhere, or do something, fast. You can also rush someone else: "Don't rush me, I like to stay after the movie and watch the credits!" It's a noun, too: "She's obviously in a rush to get somewhere." A "rush job" has an immediate deadline, and "rush hour" is the busiest time of day for drivers in a rush to get to work, or to go home afterward.