"MD PA" stands for Medical Doctor, Professional Association. The "Professional Association" designation is a legal term used to describe a separate legal entity, much like an incorporated business.
A professional association is a form of incorporating a group of professionals. It can include dentists, accountants, attorneys and doctors. It is a form of legal protection against lawsuits for individuals within a group practice. A suit would have to be taken out against the association rather than an individual.
In the medical profession a PA can also mean practice assistant or physician assistant. These are individuals who can practice medicine under the supervision of a physician.