The time we sleep is the time when we are the most relaxed as well as the most unguarded of our feelings as well as body language.
And if you are sharing the bed with someone else, especially, if he/she is your partner, your sleeping position can indicate the relationship equation between the two of you.
If you both sleep totally entwined with each other it indicates full on intimacy that usually comes with new relationships. But if both of you are sleeping on opposite sides of the bed face opposite as well, it might indicate that you both are quite individual personalities as well as practical by nature but yet share a very intimate relationship.