It is to do with the weight of the baby and the uterus pressing on to some nerve or artery and making your blood pressure drop.
I slept on my back right to the end of my pg with ds with no trouble.
However, this time, I am almost 35 weeks and have just been in hospital for surgery on a broken ankle and had a couple of incidents of low blood pressure.
The first was when i was going into theatre. The anaesthetist had already propped me onto my left hand side, but I started feeling faint and dizzy. This passed when he propped me further up on my left side.
The second incident was about 24 hours after surgery. My blood pressure dropped to 90/50 and I felt sick/dizzy/faint/clammy. My leg had been so sore, that there was no way I could tilt it to lie on my side, so I had spent 24 hours either on my back, or sitting with my leg up in a kind of squashed position. By this time, the pain was less, and I had a better plaster cast on, so I was able to turn on to my side and relieve the symptoms.
So, in my case (and in my case only, won't speak for everyone), yes, it did cause a problem, but it was an extreme circumstance.