If you are successor to the throne, that means you're next in line when the current royal has to step down. The successor takes over when someone gives up a position or title or when something becomes outdated.
The noun successor was first used in the 13th century to mean "one who comes after." It's often used in reference to a royal court, where the successor is usually the king's eldest son. If something happens to the U.S. president, the vice president is the designated successor and will assume the position of head of government. It seems like every day there's a new and improved computer, a successor that replaces an earlier model.