D.O. stands for Doctor of Osteopathy. These are fully licensed medical professionals who practice Osteopathy. Another way to refer to D.O.s is to call them Osteopaths.
Osteopaths are equivalent to medical doctors, as they are licensed to peform surgery and to prescribe medicine.
However, Osteopaths take a holistic view of the body as an integrated system, where an abberation in one area will have an effect on other areas.