It's because the inferior vena cava taking blood back to the heart is on your right. If you are on your left side, that minimizes the pressure on that vein. Also your liver is on your right hand side - your liver processes your blood, removing things you don't want in there, and staying on your left ensures you don't reduce blood flow to that organ.
Exactly what bumpy cat said. It's bad for the placenta therefore bad for the baby. Also makes it harder for your heart to pump blood to the rest of your body if you had pressure on the inferior vena cava.
If you have been told that your inferior vena cava is on the left side then you should lay opposite of that.
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