Rigging is the process of setting up bones to deform (bend) the mesh of a model similar to how real bones in a person's body do.  It is done in the Setup room and with the Joint Editor in Poser.  In DAZ|Studio you have to look into the Figure Setup Tools, these are not included in the base version, although there is a minimal version that is pretty cheap ($15).

http://www.youtube.com/watch?v=q8jxSOL_MAM (Phil Cooke's rigging tutorial, part 1 of 3, watch all 3)

Stuff that has bones is called a "Figure" and is usually listed in Poser's library in the Figures section.  Stuff without bones is called a "Prop" and is listed in the Props section.

Conforming clothing is a model of a piece of clothing that is rigged the same way the character figure is rigged, so that it can be Conformed onto the character, and then the character can be posed and the conformer will follow the same pose automatically.  For this to work, the rig (the skeleton, the bones) has to be pretty much exactly the same as the character figure, although it can be extended for things like skirts or pieces of the garment that stand away from the body.  All the major bones, like the shoulders and thighs, have to be positioned and sized the same as the character figure, or when the character is posed, the garment won't bend the same way.

Also, the mesh (the polygons, the geometry) has to be positioned appropriately for the bones to affect them; if you're converting a garment from one figure to another, and you adjust the rig but you don't adjust the mesh, then the polygons of the garment will often be too far from the bones that should bend them, and the polygons won't be bent as the bones move.  This is what is meant when people say the base mesh of the garment has to fit the "base morph" of the target character.  This is also why, when you're modeling a garment, you have to use the default un-morphed un-posed character figure as a reference.  If you model a garment around a heavily morphed character, it will be much harder to rig... as I realized on this project - it was one of my first and I didn't know any better, so later on when I had done a few more things THE RIGHT WAY, I realized why it was so hard to rig that earlier one.

The big difference between Morphing Clothes and stuff like Crossdresser is that Morphing Clothes does not touch the bones, it just adds morph targets to a garment.  If the rig (bones) of the garment does not match the rig (bones) of the character it is conformed to, it isn't going to pose correctly even if the morph fits perfectly at zero pose

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