BREP is short for Boundary Representation. A BREP reproduces the precise geometry when exporting IFC files. BREP geometries will include Solid Element Operations, Trims, Crops, etc from the ARCHICAD model.
Example of an ARCHICAD IFC exported as Extruded/Revolved geometries (Revit 2016). With the extruded/revolved geometry method, elements edited with Solid Element Operations will be exported according to their original definition geometry – as for example on this image.