Let me take a stab...
A wet/dry filter is essential one aimed at providing a medium for optimal growth of the beneficial bacteria that oxidixes ammonia into nitrites and then nitrates. It is generally designed such that the filter media has extensive contact with the air as well as with the water.
Some versions of these include filters that trickle water over the filter medium (a sump full of bioballs; a biowheel) where others (notably the Eheim wet/dry canister) cyclically fill then drain the canister, exposing the medium to oxygen, then water, etc.
The key is that their is availability of high oxygen levels to facilitate the biofilter's action.
Generally, some sort of mechanical filter precedes the wet/dry portion, to help keep the bio media a bit less clogged.
Hope this helps,
Jim