The concept is pretty simple: you take two nodes, you have them "stick" together (think snapping), and when you move the other node directly or indirectly (moving the whole object), the other node stuck to it moves along.
Same with segments. It basically makes a copy of that segment and its handles, and sticks all of them together.
Same with whole objects actually, I forgot that one, you "snap" the whole object onto a point.
Background: I mainly came up with the concept because I like (trying to) do drawings with complex strokes. The new LPE interface makes the complex strokes a lot easier, but if you actually want to fill anything in between, you have to edit the strokes And the fill (basically doubling the edit time).
Now, you Could tell me to just deal with it and/or delete the fill and make a new one, but it becomes a whole other story if Inkscape wants to include animation one day, so consider this a preliminary feature:
http://img373.imageshack.us/img373/2604/stickynodesja9.png
The problem is the interface. We could have a sub-mode of Edit, or a whole new tool, and of course we'll need shortcuts. Then for that new fill option, a new option would have to be added as well. I'm still pondering the matter (as well as the text tool interface), but maybe some of you have ideas already? This way at least we could discuss the blueprint. Maybe when Summer of Code 2009 comes around, some student would be interested and take up the whole thing! :)