This is such a witty little allegory that Henry Tilney spins for Catherine. He prefaces it by saying

"That gentleman would have put me out of patience, had he stayed with you half a minute longer. He has no business to withdraw the attention of my partner from me. We have entered into a contract of mutual agreeableness for the space of an evening, and all our agreeableness belongs solely to each other for that time. Nobody can fasten themselves on the notice of one, without injuring the rights of the other.

Now, this is certainly an occasion for Henry to display his wit for a receptive audience, but I wonder at the impetus for it. Henry and Catherine are standing up together waiting for the dance to begin when John Thorpe barges in and harangues her with the belief that she should be dancing with him. I mostly believe that Henry is trying to distract Catherine from Thorpe's boorishness, but I also wonder if he is not displaying just a tiny niggle of jealousy? Especially when he ends his allegory with

"Have I not reason to fear that if the gentleman who spoke to you just now were to return, or if any other gentleman were to address you, there would be nothing to restrain you from conversing with him as long as you chose?"