Emergence is a phenomenon that intrigues me... It's quite easy to understand:
From the simple individual behavior of agents, acting locally, a global new behavior emerge from the swarm (possibly with different properties and characteristics).
Consider an "Ant Bridge":
Each individual ant is acting based on some rule like:
"reach the edge, there hold the last one"
They really don't "know" they are making a bridge, they just do it.
Following this behavior they eventually reach the other side forming a bridge. So the bridge itself is an emergent sequel of a simple behavior that had nothing to do with bridges!
I consider those kind of solutions extremely beautiful, not only because it's generality, but because the fundamental behaviors are quite simple and the combination of locally aware agents following the same simple rule solve a much more complex problem.