The heat causes them to rise and they form a cap, with all the solid particles that rises to the top. If the liquid is drawn off without disturbing this cap, it will be seen to be water clear. For chicken consomme, I grind legs and thighs of chicken, bones and all. Of course, the best thing to use would be an old rooster, but you can't get them any more. The meat is so tough as to be useless, but it has great flavor.
Flavor is why the meat is used.
In the cooking it gives up the deep rich meaty flavor that makes consomme so grand. When I want to make a really strong consomme, I cook oxtails in the stock to extract their flavor. As a matter of fact, this is what I call my change the flavor technique. First make a good rich white stock of beef and veal, and then add roasted duck or lamb bones, and cook for an hour or so, which is enough to pick up a pleasant flavor of the strong flavored duck or lamb. When I say it is infinitely adaptable, I mean that there are a large number of garnishes that can change the name of the soup.