Basically, by moving the lens vertical axis relative to the body vertical axis, you are moving the plane at which things are in focus. This way you can, say, shoot a model full body and yet have the face in focus while the rest is not. Also, small amounts of light creeping in the openings will create a kind of "ethereal" effect on the photos. You can see great examples and a guide to freelensing here: http://www.bhphotovideo.com/insights/blogs/photography/how-freelensing.html . Another application could be "Miniature faking" (see here: http://en.wikipedia.org/wiki/Miniature_faking) - basically defocusing a normal photo in a way such that it seems to be a macro photo of some miniature instead of reality.
To do this (the non-parallel plane of focus) in a more traditional way, usually tilt-shift lenses are used; they are very expensive lenses, made to be as free as possible from deformations of the resulting image and used specially in architecture photography. Other solutions are lenses like the Lens Baby system which enable this kind of effects.