Dr. Ross McKenzie has provided a definition of emergence on his blog, Condensed Concepts. This definition nicely summarizes and simplifies emergence by laying out the properties that describe emergent phenomena.
I've always struggled with defining emergence because it seems that a definition by example is the best way to do it, but this is often difficult to do simply. Trying to define emergence in one sentence, rather than the list that Dr. McKenzie provided, seems nearly impossible. There's always some form of discussion that's required.
What other kinds of models or theories require expanded definitions involving enumerations of their qualities?