Music and dance are two uniquely human phenomena. Though a number of animals employ seemingly rhythmic calls or bodily posturing, in non-humans, such behaviors are instinctual and "pre-programmed." What really sets rhythmic human motion and sound apart is the capability to be creative, drawing from set rules of aesthetics.
Music and dance are akin to human language in that they creatively arrange and rearrange a variety of "chunks" of information- sounds for music, and movements for dance. There is another phenomena which occurs in human language which I believe relates music and dance to one another- connotation. In language, words and phrases might conjure up a natural feeling or implication of other terms. For example, the word "coffin" has connotations of death and perhaps the afterlife. So, too, in music and dance are there connotations. It is more easy to connote movement with sound, as a short, shrill violin shriek might imply a jerky, sudden movement of the body.
Try this experiment: click here for a link to listen to "River Flows in You," by pianist Yiruma. Close your eyes while listening and allow your body to relax. Does the music give you a sense of movement anywhere in your body? Do you have the urge to move in a certain way? If not, you might imagine a little dancer in your mind- how do they move as the song plays? Slow, fast? Hard, graceful? With levity or labor? The rhythm and pace of music, the key notes are played in, and the choice of instrument can all inform stylistic choices in dance.
With that in mind, the origins of dance are mysterious, but we suspect that it developed following or in close relation to the development of music. Dance does not leave behind much archaeological evidence, but historical paintings of Greek and Egyptian dance very closely associate it without music. Even in a time before instruments, people may have clapped hands, sang, or stomped feet to provide rhythmic accompaniment to dancing.
Today, it is difficult to separate music and dance from one another. The two are bound together in their religious, social, and performative significance.