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This object property lets you specify the an objects bounding box/bounding sphere, or plane as a cutting object in your scene. Any objects inside the cutting objects bounding box/sphere, or behind the specified plane will be disregarded when rendering, rendered as if it wasn't there. This is different than was hidden from the camera, just as with the Z-clip planesfeature of the Camera properties because Z-clip simply hides the geometry to camera while that geometry still influences the lighting in the scene. Taking the car example from the Z-clip page, this image shows you the difference between cutting out parts of the care using the camera Z-clip planes and the Boolean property set to "Plane ZX" for a polygon plane in the scene:cameras. The two big advantages compared to z-clip of course is that you can freely move the camera without affecting what gets clipped, and also that you can create different sizes and shapes to act as clipping shapes.
Bounding box
This option takes the bounding box size of the object and uses it as the cutting shape.
Bounding sphere
This option takes the bounding sphere size of the object and uses it as the cutting shape.
Planes
This option is easiest to use if the geometry is already a plane. It will make everything in the negative direction of the chosen local axis (XY, YZ, ZX), hidden to the camera. You can rotate the object to decide which way the negative axis is pointing.