MBR is used for extent of geometries.. then what is the use of MMP.. is it for visualization the objects?
It's hard to determine from that link what MMP actually is. It seems to me it's like this.
You want to know whether the line intersects the polygon
Standard practice is to create a bounding box and see if they overlap. If not, there can be no intersection. If they do then it may intersect and you do a full intersection test to check.
With MMP you replace the start/end point of the line with point features and test if they are inside the polygon. If only one is then you know there is an intersection. If neither or both are then you then do the full intersection test to check.
So it's basically a way to reduce the need to do full intersection tests. At least that's how I read it. Quite a good method really, though whether it warrants a patent I'm not sure.
I couldn't find much on MMPs (Minimum Maximum Points) and geometries in a GIS context. According to a patent text found here: http://www.freepatentsonline.com/6438269.html, MMPs are a generalization describing geometries (lines and/or polygons) in a way to increase performance of spatial filters.