By rapport, I believe the author means non-verbal cues that the other person is interested.

Some cues include the person physically squaring up to you front to front instead of being at an angle to you. Another cue could be touching you on the shoulder or forearm. For me the most obvious tell is that they are laughing or giggling.

Breaking rapport means the other person wants to disengage without offending you. I usually make the excuse I need to take a breather.