COLLADA is short for Collaborative Design Activity. DAE files are based on the XML COLLADA format, and they are used by various graphics programs to exchange digital assets under the same format. Each file consists of a set of elements that are images, lights, geometries, effects, materials, cameras, etc.
Many elements in Teigha BIM contain B-Rep geometries in GElement, which is a geometry cache of an element. However, B-Rep is not a universal format. Each product has a specific representation of B-Reps.
An overview of B-Reps and BIM specifics can be found in the documentation (login required).