There is an easy physical explanation for the contagiousness of yawns: When you yawn, you equalise the pressure between your inner ear and the outside world. This is why yawning helps when your ears are popping, on an aeroplane or in a train tunnel for instance.
But of course, when you equalise the pressure in this way you cause a change in the pressure of the surrounding air. This means that the pressure in the ears of people nearby no longer matches the pressure in the air around, so they have to yawn to compensate. If there are more people around, you can set off a whole chain reaction.
So there you have it.
...and if you have a better explanation of that I'd like to hear it.