An Adjutant-General is the chief administrative officer of a military formation. Adjutant-generals take charge of personnel matters such as postings, transfers and assignments, the proper keeping of personnel records and the welfare and morale of servicemen. The term describes a job position and not a rank, so an adjutant-general need not necessarily be a general, although at a high level formation such as a Corps, it frequently is. The position of adjutant-general of a unit is normally held by an officer of the Adjutant-General's Corps.
In Season 8 "Too Many Cooks", Potter's friend Brigadier-General Budd Haggerty is an adjutant-general (probably of I Corps). In this position he would naturally know about Potter's request for transfer and so came down to the 4077th MASH to see why his old friend wanted out. As adjutant-general, he would also be in a position to change Pvt. Conway's MOS (military occupation specialty) from Infantryman to Cook.
In Season 2, "Radar's Report", Frank and Margaret want a Section 8 for Klinger and threaten to take it directly to the Adjutant-General.