No aspects of the gameplay are effected by enabling this, but aesthetically there is a large difference. An nVidia card is not required to run with higher PhysX settings in Borderlands, the calculations can be done on your CPU but you will take a noticeable performance hit.
Turning the PhysX option up will effect things like cloth animation, particle effects, fluid animations, etc.
There are several videos on YouTube that run side by side comparisons of the various visual differences between the settings, here is one which does a side by side comparison with the PhysX setting on 'Low' and 'High' (the video says 'Without GeForce/With GeForce', but it has been discussed elsewhere that many users of AMD hardware are able to run the game with the PhysX setting on 'Med' or 'High' without any nVidia hardware at all).
The differences between the settings are pretty noticeable, but especially so with liquids and explosive weapons.
There is an article on the nVidia website (right at the bottom of the page) which details more specifically what the individual PhysX levels affect, along with a performance related graph comparing nVidia and AMD hardware.
Low Medium High
Debris No GPU effects Particle count reduced Max quality debris
SPH Fluid No GPU effects Particle count reduced Full range of effects
Cloth No GPU effects Low quality cloth Max quality cloth
Particles No GPU effects Particle count reduced Lots of sparks and embers
Furthermore, here is some nVidia descriptive text as to the differences between CPU based physics and PhysX, quoted from the above article:
With CPU physics, the emitted debris would shoot across the screen before fading out of existence, or in some cases, sitting motionless on the ground, unaffected by the action occurring around it. In Borderlands 2, with hardware-accelerated PhysX effects enabled, this debris will be kicked about by further weapons fire, or from characters running through it. Pieces will land on inclines and roll towards a level surface as in real life, and should another piece be in the way the two will collide, further changing their final position. Bring enough pieces together and they’ll pile up, and with the highest level of PhysX enabled these pieces will persist until removed to make room for yet more mayhem.