As a new selectee for the Navy HPSP, I, too, have been trying to figure out what a GMO is. After talking with a flight surgeon and an FP (talk to your recruiter for contacts), and doing a little Internet research (type "General Medical Officer" into google.com), let me see if I understand what it's all about.
GMO's are the core doctors in the Navy. After serving a year of internship, most HPSP docs do a GMO tour, which can last 1-4 years, but usually 2-3. These can be in clinics, bases, or on ships, and with both sailors and Marines all over the world. As a GMO, my impression is that you're an officer first, a doc second. You supervise corpsmen, who are providing most of the general care. On board ship, for example, you are (most often) the department head, and report directly to the captain and the XO. You are in charge of all the administrative stuff that happens in your department, from ordering supplies to performing inspections in the galley.
From my perspective, it's an opportunity to have a lot of fun while learning a lot about leadership and responsibility--to have the Navy experience. From the Navy's perspective, they're getting officers with medical training to oversee the corpsmen and to ensure that the sailors and Marines are combat-ready (which can lead us into all sorts of ethical debates about the role of physicians in the military, but not on this thread, please).
It also appears that a GMO tour is a gold star on your record, particuarly when applying for residencies and fellowships. The more you accomplish/the higher your praise from superiors, the greater your chance of securing that derm residency you always wanted.
Please feel free to clairify or correct anything I've said. (I just felt compelled to answer this question before the tread went away.)