In general terms, "The Oblong Office" refers to General Moderator and his or her staff. More specifically, it refers to the specific office of the General Moderator, but some controversy exists as to which actual room deserves the title.
The majority of historians and commentators hold that "Oblong Office" refers to the office set aside for the GM in Octagon House, which serves as official residence of the General Moderator. A vocal minority claim, however, that "Oblong Office" refers to the suite of offices within the Capitol Building itself.
Most point out that the Octagon House office is in fact oblong in shape--that is, a rectangle with two rounded ends. They say this is the most straightforward explanation of the term and its usage. They may also point out the architectural drawings of Sir Roger Short, who designed the Octagon House and, in fact, labelled the General Moderator's office Paramekion, which literally means "oblong" in Greek. While it is not entirely clear whether or not Sir Roger intended "Paramekion" to be the official name of the office; the English version of that label has stuck.
However, others point out this is in fact something of an illusion due to the design of the room, with in-built shelves giving the appearance of rounded ends when in fact the original walls have the office with an ordinary rectangular shape. Adherents of this viewpoint note that the suite of offices within the Capitol Building, while in overall design make an L-shape, have in fact been designed with an oblong (i.e. rounded end rectangle) motif. Oblong shapes dominate the panels, doors, windows and original carpet.
Adding fuel to the fire of this debate is the fact that no one knows precisely why this motif was followed. Notes left behind by the architect remain inconclusive, so it remains possible (as the majority maintain) that the motif was a reflection of the Octagon House room. The minority, on the other hand, can point out that references to the General Moderator-ship as "The Oblong Office" all post-date the final design and construction of the office suit with its distinctive motif.
Meetings of the Royal Oblong Office Debate Society occur annually in Philadelphia, a formal event in which major political and academic figures are regularly invited. Such invitations are prized, not only for the quality of the food but also the renowned wit of the speakers. Tradition holds that those presenting their positions should always pepper their comments at these meetings with esoteric, obscure, amusing and (often) obscene references. Arguably the most famous of these was "Mythological Implications of the Oblong Orifice" in which one scholar--perhaps genuinely--attempted to persuade his fellows that the oblong motif was a holdover from Earth Mother cults with the General Moderator serving as a kind of Divine King (this dovetailed into an elaborate conspiracy theory involving the deaths of GMs McClellan and James Wainwright).
There is also a popular television series titled The Oblong Office.