What exactly does it mean to rig 3D models?

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Rigging is making a 3D model so that you can move it (such as move its arms, make it walk, etc). To rig a model, you make a skeleton for it (basically like a real skeleton), then you tell the computer which parts of the model to move when you move each bone. In Blender, a skeleton is called an armature, and the process of telling the computer what parts to move when you move each bone may be done by weight painting, or by manually making vertex groups that have the same name as their respective bones. For more information, I recommend the Blender wiki (wiki.blender.org) -- it even has a very detailed step by step tutorial on making a basic character, from modeling the character to rigging and animating it.