To be stately is to appear noble and impressive, almost in a larger than life kind of way. You may encounter a stately gentleman or a stately statue. If you do, take a little bow.
There are a few meanings of stately, but they both refer to people and things that have an impressive bearing. The first meaning has to do with nobility and class. A ceremony honoring a prince is stately, and the music and dress surrounding such events are stately. Stately things convey sophistication and regality. Also, stately can mean statuesque. Someone with great posture and an impressive physique is stately, almost as if they were made by a sculptor.