Bound has several distinct meanings:

1. To leap or jump energetically. A dog might bound across the yard when you come home, springing forward with powerful jumps. Deer bound through the forest in graceful leaps. When you see someone bounding up the stairs two at a time, they're moving with energetic, jumping steps.
2. Certain to happen or required to do something. If dark clouds fill the sky, rain is bound to fall soon. When you promise to help a friend, you're bound by your word to follow through. A student bound for college is headed there with certainty. The phrase duty-bound means obligated by responsibility or honor.
3. Tied up or restricted. A prisoner might be bound with ropes. Books are bound together at the spine, their pages fastened permanently. When someone feels bound by rules, those rules limit what they can do. You might also be homeward bound, meaning traveling toward home, or bound for a destination.