Basicly It is where Battlemages are trained for the Imperial Legion with help from the Mages guild. In all of Oblivion there was one permanent battlemage, stationed outside the Arcane university. I guess the battle-school is somewhere in the Jungle.
There's actually quite a sizable http://www.uesp.net/wiki/Category:Oblivion-Battlemage of people in Cyrodill who were trained as Battlemages at the time of the Oblivion Crisis.
Of course, I doubt very many of them were from the Battlespire, as they were alive and too young to have been trained there. I believe Ocato and Dagail are old enough to have been graduates, but very few of the others would have been advlts at the time.
It's likely that the Legion found a new place to train Battlemages after the Battlespire went down, and that some of the people classed as Battlemages didn't receive any official training for the Legions, since some of them are mercenaries and criminals.