It would certainly take a masters dissertation to answer such a question, but even so, I am surprised that no one has responded.
This seems to me to be a controversial but desperately important issue.
As dancers, we call ourselves artists rather than athletes and frown upon comparisons to gymnastics, ice-skating, synchronized swimming, etc.
But what exactly separates dance from sports such as these?
For me the distinction is emotional resonance and intellectual stimulation. The above mentioned sports can be very beautiful, technically virtuosic, entertaining, etc. but I am unable to build any personally relevant connection to them. I can find no meaning behind the movements.
A single movement in unto itself has no meaning or value. It is the context in which the movement is placed and the way in which the movement is executed that enables those watching to assign meaning and value to it. For example: We have all moved from parallel to first position a million times without even thinking, but when a this simple movement is performed in the opening of Serenade it is very striking and vitally important to the ballet. So you see even in completely abstract dance the audience can identify with the structure, patterns, spatial relationships, movement dynamics, etc. and the audience can sense an overall atmosphere or mood created by the choreographer.
The oft-repeated cliche is that "dance is a language."
In every dance something is being communicated by the choreographer, through the dancers to the audience. (Even if it is simply the beauty perfectly organized space and time.) Otherwise why would he/she take the time and energy to put it on stage? And why would we bother to watch it?
What is the difference between music and noise?
Even silence can be meaningful, if put in context.
For example look at John Cage's composition 4 minutes 33 seconds.
A musician enters the concert hall, places violin to chin, raises the bow, and does nothing for 4 minutes and 33 seconds. He then puts his instrument away and bows.
The composer is certainly making a statement with that!!!