Military Assistance Command Vietnam, Studies and Observations Groups, or depending on who you talk to the A was for Advisory. The details about MACV-SOG are a little fuzzy. Some of their operations are still classified and the unit had an unusually high attrition rate due to the dangerous nature of their missions, so there really aren't alot of people coming forward and talking about it. There are far more pretenders who will tell you they served in MACV-SOG than there are survivors.
MACV-SOG was a joint operations unconventional warfare unit that engaged in highly classified support missions throughout Southeast Asia. The ranks of MACV-SOG were mostly funneled through Special Operations Augmentation from the 5th Special Forces Group. MACV-SOG wasn't entirely a green beret operation though, some of the ranks were filled from other units and they were occasionally supported by "CivIlian Advisors."
The MACV-SOG mission fluctuated as the need arose, but most of their goals were reconnaissance and interdiction behind political boundaries that the US could not be seen to officially violate during our time in Vietnam. Most of these missions went deep inside Cambodia, Laos and North Vietnam to both gather information and raid targets that were offering support to the North Vietnamese Army. In 1969 alone MACV-SOG performed 452 such operations. This was one of the most sustained operations of sabotage and reconnaissance performed by a US unit on foreign soil.
As the conflict in Vietnam ended the role of the MACV-SOG unit was phased down, but it remained clear that such a unit had it's benefits. The joint task force was reorganized into the SOG, now Special Operations Group, and it often recruits from the various US Armed Forces.