When you are pregnant sleeping on your side is thought to maximise blood flow and oxygen to your growing baby. Research shows, from about 28 weeks pregnant, you should start to go to sleep on your side, either side is fine. When you wake up on your back, just roll-over onto your side again. Falling asleep on your side, means you stay on your side for the deepest and often longest part of your sleep.
Sleeping on your side in pregnancy has the potential to reduce late term stillbirth. 
 McCowan, L, et al. (2017) Going to sleep in the supine position is a modifiable risk factor for late pregnancy stillbirth; Findings from the New Zealand multicentre stillbirth case-control study.