It is recommended that you sleep on your left hand side for the following reason....
There are big blood vessels which run from your heart, (in the the middle of your chest) down your back to just below your belly button where they divide into smaller tubes. Your womb and baby lie in front of these blood vessels and when lying on your back their combined weight can squash these tubes and affect the way blood flows around the body. A bit like standing on a hose pipe.
If these blood vessels are squashed you may feel faint, dizzy and sick as there will be less blood flowing to your head. If you feel like this then there is also less blood flowing to your placenta and baby.
Lying on your side takes the pressure of your womb and baby off these blood vessels. These blood vessels lie a little to the right in your body hence the advice to lie on the left. The further on in pregnancy you are, and the bigger your womb and baby, the more likely you are to be affected.
However, lying on your right hand side if more comfortable is fine and you can't control what happens when you are asleep, so just try to start off on whichever side feels more comfortable.
If you notice that you feel faint when lying on your back the advice to lie on your side is even more important. Try using pillows to stop yourself rolling over.
I hope this helps.