"Dawn Magic" could be interpreted to mean magic which was known first in the Dawn Era... or it could relate to forms/techniques/understandings of magic which, in their application, affect reality in a fashion akin to the instability of the Dawn Era, such as supreme manipulation of space-time, the bending/nullification (however temporary) of the Earthbones.. temporarly removing Lorkhan's sundered corpse from the sky only to bring it back... or it could just be a BS term haughty altmer use as handwaving.
Edit: I would hesitate to apply the label of "Dawn Magic" to the Thu'um, however. While it might have been practiced pre-convention, it just doesn't seem quite right to call it such. Dawn Magic has merrish conotations.