What is this architecture feature called?

I'm not sure what you're referring to here, but the structure extending perpendicular to the main roof plane would be a dormer. The overhang past the the walls would be the eave (dark brown portion). The underside of the eave would be the soffit, and the vertical face of the eave would be the fascia. Gable would refer to the roof design, but you are right in that it is a gable styled dormer.