From LightWiki

Named after famous 19th century English mathematician George Boole Boolean operations form the basis of modern algebra and are used to indicate functions that cut or add geometry in LightWave.

This is the base geometry in LightWave and the four Boolean operations.
Boolean Add Both geometries cut into each other's surface The internal geometry of both remains.	Boolean Subtract One geometry is removed from the other, leaving a gap or hole.
Boolean Intersection Only the volume contained in both geometries is retained.	Boolean Union Both geometries cut into each other, but all internal geometry is removed.

Booleans should not be used where geometry will be subpatched since boolean operations often leave polygons with more than four points behind. You should also clear up after a Boolean operation (merging points, checking for single-point and two-point polygons) since they can be quite "messy".