The reason is not entirely clear. One hypothesis holds that:

The reason is not entirely clear. One hypothesis holds that right-side sleeping relaxes the lower esophageal sphincter, between the stomach and the esophagus. Another holds that left-side sleeping keeps the junction between stomach and esophagus above the level of gastric acid.

http://www.nytimes.com/2010/10/26/health/26really.html?_r=0