Yawning was for humans, and in some species still is, a signal to others in the group that it is time to go to sleep. Group's that 'bedded down' together not only reinforced the group bond, and individual bonds between members, it also ensured no member was left out alone, susceptible to predation.

So when one member yawns, and a chain reaction is set off, everybody realises it is time for bed and survival chances are increased.

Yawning is also a sign that your brain is tired and is in need of more oxygen, hence the long inhale. So as one person yawns to get more oxygen, another person also recieves the signal, as their brain also starts to think it is tired and causes you to yawn :)

Humans have a subconscious need to show that they fit in with other people and for that reason we will not only yawn when someone else yawns, we will do things like scratch itches, swallow, and blink when someone else does, particually our superiors. Most of the time when we do this we do it without even realising. Next time you are with company, you could put this theory to the test by scratching your head or something. (I wouldn't recomend farting or burping but you never know, they might work as well)

Contagious yawning has not been fully understood by science yet.  There are numerous theories on Sleepyness, but if it is a signal to go to sleep then why do you yawn in the morning? or before a big event when you are not tired.

There have also been studies that altered the levels of oxygen in a room with no significant change to the frequency of yawns in those with less or normal oxygen levels.

It may be a vesitigial behaviour from the past, and when someone yawns you empathise with them and copy their behaviour subconsiously. But the reason is not definitive why you yawn in the first place.

It's not just humans that find yawning contagious, chimps also demostrate this. I liked this article from the BBC which shows that chimps can "catch" yawning" from animations.

http://news.bbc.co.uk/2/hi/science/nature/8244963.stm