"Tell me what it isn't!"
The examples I gave, superconductivity and ferromagnetism, are example of phase transitions, which only happen when there are large number of components interacting. I wouldn't call phenomena that can be explained by one or few components as emergent. So, I wouldn't call a black hole as emergent. I wouldn't call an electron and a proton making up a hydrogen atom as emergent. I wouldn't call two hydrogen atoms and an oxygen atom forming a water molecule as emergent. But liquid that is formed by a large number of water molecules is an emergent phenomenon to me. Jagadul's example of traffic jam is also a good one.
Aren't superconductivity and ferromagnetism perfect examples of emergent phenomena? I'm not saying that calling something an emergent phenomenon adds any deeper understanding of it. But I think there certainly are phenomena that can be fairly called as emergent.
I disagreed Rip's opinion that black holes etc. are examples of emergent phenomena, but other than that I don't really see much disagreement about what emergence is in the comments here.
I like Zubon's description "the whole is not predictable from the parts" and "No cell in your brain understands Chinese,..., but the system as a whole does."
Why can it be useful? I can think of two possible reasons. There is a certain reductionist tendency (although I don't think being reductionist per se is bad) to assume that we get better and better... (read more)