Heart
Your heart is on the left side of your body and when you sleep on your left side, gravity pushes the lymph drainage toward the heart taking off some of the workload as you sleep.
Spleen
Your spleen filters your blood and when you sleep on your left side, drainage back to the spleen is also helped by gravity.
Stomach
After a meal, you can benefit from getting a boost of energy by lying down for 10 minutes on your left side. Your stomach and pancreas hang naturally, which allow you to digest your food more efficiently. Sleeping on the left side allows gravity to move food waste easily from the small intestine to the large intestine. By the time you get up the next morning your colon will be full, which is why you have to go to the bathroom first thing in the morning.
Liver and Gallbladder
Your liver and gallbladder are on your right side, so resting on the left side allows them to secrete precious bile into the digestive tract and blend fats and neutralize acids found in your stomach.
Interestingly, a recent study found that people who sleep on the right side of the bed tend to earn more than their partners at the left. Left side sleepers on the other hand are more cheerful and have a more positive attitude.