I'm a third year med student, I don't have a very good answer for you, and I'm not sure that it can be answered physiologically, but I do think it is true that people subconsciously incorporate behaviors that they see into their own actions very often.
When I'm in the hospital on rounds I spend a lot of time standing around in a circle talking/discussing patients, and I've noticed that whenever one person assumes a certain posture say crossing their arms, within a minute several of the people in the group will also cross their arms.
This is what google came up with for me:
http://www.al.com/healthfit/mobilere..._307yawns.html
I also remember that Malcolm Gladwell's book The Tipping Point had a section talking about infectious yawning, although I don't think he offered an explanation for it.