That dragon is of Akaviri origins, and I believe it depicts Akatosh, ultimate patron of the Empire. It is the most powerful symbol in existance for Imperials and followers of the Empire.
http://i32.tinypic.com/mmzb69.jpg
The symbol originally is intact and has a diamond over it. The diamond alludes to the large red gem inset in the Amulet of Kings http://images.uesp.net/thumb/2/26/OB-item-Amulet_of_Kings.png/180px-OB-item-Amulet_of_Kings.png, which http://www.imperial-library.info/category/tags/amulet-kings. This diamond is a representation of the royal Septim lineage, i.e. the line of Emperors. The dragon refers to Akatosh's blessing of this Septim lineage and symbolises the Empire. The entire symbol represents the Empire and the Septims which rule over it. It appears in Morrowind (it's even on the cover) and was all over the place in Oblivion, http://images2.wikia.nocookie.net/__cb20060321171447/oblivion/images/thumb/4/42/Septim_coin.jpg/800px-Septim_coin.jpg, as OP has seen (no suprise given that Oblivion takes place in Cyrodiil, the heart of the Empire).
http://thingiverse-production.s3.amazonaws.com/renders/60/1c/c5/f4/89/skyrim_display_medium.jpg
This is the symbol as it appears in Skyrim. Contrary to popular opinion, it doesn't refer to the dragons of Alduin, but rather to the precarious nature of the Empire circa 4E201, when Skyrim is set. The symbol is partially broken on the lower right tip, an allusion to the Empire's weakened state following the Oblivion Crisis and the Great War, and, importantly, the Alessian Diamond is missing - a direct reference to the breaking of the Septim lineage (following the assassination of Uriel VII, his three sons and the martyrdom of his illegitimate heir Martin in Oblivion). The Empire in Skyrim is ruled by the Medes, a Colovian family which bear no familial bloodline back to Alessia and so do not have 'dragon blood' or the blessings of Akatosh. Many suggest this ignoble leadership is somewhat illegitimate and that the lack of a Septim Emperor is why the Empire is in it's current weakened state.
(Sorry, image tags didn't work, so you'll have to make do with links.)
Hey, none of that imperialistic propaganda around here!
Careful, you. This is the board for Oblivion, a chapter which fully revolves around Cyrodiil and the Empire. As a proud Imperial, I'll have no secessionist talk here