Firstly this copies in data that may be needed to render the triangle, such as uv co-ords etc into a structure which is passed to the triangle painter. Just my uv co-ords etc are stored in triangle structure, so they need to be copied. If it does need to be clipped however, it calls a clipping routine, for the related rendering mode. Eg if rendering for texture, it calls ClipTexture, for gouraud, it calls ClipGouraud, and so on. It only needs to be outside of one plane to be discarded.
Bounding boxes are also pretty easy to do.
You can just check the 8 vertices of the box, and see if at least one of them is on the positive side of the plane. That way you can get away with less checks, if you're clever. I hope this web page has provided you with enough information for clipping polygons against planes, specifically the viewing frustum. If you have any questions, mail me.