The core concept behind that is when simple systems come together to create complex decisions. In other words, the rules aren't that hard but they allow for tough choices. You know, a minute to learn but a lifetime to master.
Go is the poster child for this. The rules to go are very simple. I once heard someone summarize them in about six sentences, with two of the sentences being there is a 19 x 19 board and the players use black and white stones. However, Go creates amazingly complex situations. A 19 x 19 board is actually a huge playing area and allows for elaborate patterns to form.
However, there is another side to emerging gameplay. That is when the interaction of the players with the rules creates unusual or even unexpected results. This is something that video game community has become fascinated by. Heck, I would even go so far as to say invested in.
But this aspect of the emergent gameplay is also very important to role-playing games and even board games. Honestly, the sandbox nature that is intrinsic to role-playing games actually makes this pretty much what role-playing games are about. They also play an important part in boardgames, although the tighter framework of boardgames makes this kind of a emergent play a little more restricted.
But it's still definitely exists. Back to my example of Go above. Over the many centuries that Go has been around, a lot of formula has been developed. There is a term called Joseki, which means an established pattern of play that that would work well for both players. As a sidenote, even though I did Go for a few years pretty heavily, I was never anywhere near understanding Joseki.
But there is another concept called the Divine Move. That is when a single move, one that is inspired and anything but obvious, can turn the game around. They are said to be so rare that a professional Go player may play one only once in her or his life.
But they exist. Or, a lot of Go authorities say they exist and they know a lot more than I do.
And when games allow for more flexible interactions between the players, this kind of emergent gameplay becomes more possible.
Both of these aspects of emergent gameplay fascinate me. They define the depth and the surprise of playing games.