At the time, jazz music was the popular music heard on the radio. The dance steps took on the name jazz because of jazz music. Pretty simple actually. Ballet is easy to recognize. As soon as you see the turned out feet, hair in a bun, and fancy arms, you know that you are watching ballet.
Jazz is tougher to figure out.
It is a label we put on dances seen in Broadway shows, MTV videos, concert dance companies like Hubbard Street, street dancers, drill teams, and tap dancers. While these styles seem very different, they all have a common root. The key elements of jazz music are syncopation, individual style, and improvisation. The original jazz dancing carried these same elements. Syncopation is what gives jazz music and dancing its edge and excitement.