My understanding is that the action of the spiders exerts force on the clutch pack to lock it up. The tighter the pack then the less slip it has in the unloaded or light load condition. When one wheel is spinning, it puts rotational force on the off side. That rotation causes the spiders to "climb" on the idlers forcing side play against the clutch pack.
This may be the best explanation of how it actually works
http://en.wikipedia.org/wiki/Limited_slip_differential