http://lesswrong.com/lw/iv/the_futility_of_emergence/ In the comments, the author asks: what *isn’t* emergence? Some people have contested his definition (or rather, his understanding of how some people define emergence).
Seth Hearthstone addressed this matter as it applies to games fairly well before me: https://sethhearthstone.wordpress.com/2011/04/07/of-emergence-and-exploits/
I’m going to limit my explanation here to games, I believe emergence is a phenomena that exists. I believe it’s a phenomena that is critical to understanding depth. The quintessential engineering goal of games is to produce a large number of distinct outcomes, while keeping the apparent structural complexity of the game low.
For example, I’d cite visual novels as having a low factor of emergence, because the number of outcomes relative to the number of choices is usually 1:1 (though some of course carry over variables, and modify parts of the script based on circumstance). Point and Click adventure games similarly have a low factor, because the majority of interactions between objects are invalid, relying on you to find the valid ones.
To give a simple example, you have rock paper scissors, which has 3 essential elements, that can produce 6 possible outcomes. Interaction of elements to produce a large number of differentiated outcomes is a thing that can reliably be planned for and evaluated. A term used in a similar context is Possibility Space, referring to the range of possibilities created by a system.
The product of a sufficiently complex system is that among the outcomes that emerge from it will be outcomes you could not necessarily foresee. If a system is simple enough that the designer can foresee each individual outcome (at least those significantly differentiated from one another), then as a rule of thumb it is likely to not be a system that will hold player interest for long.
I would personally avoid conflating emergence with unpredictability. I think trying to judge a facet of an object for intention or foresight on the part of the designer is pointless, and emergence is a thing that can be engineered for by creating mechanics that affect variables inherited by or shared with other mechanics.
I actually discussed how this article from Less Wrong made me feel uneasy with a friend fairly recently. It’s primary purpose is to prevent people from using a buzzword as a substitute for a specific explanation, which is sensible. However at least in the field of video games, there is a clear delineation between things that are apparent results of the combination of mechanics (like wavedashing) and things that are arbitrarily implemented (like the properties of a Forward Smash attack). There isn’t an underlying mechanism that determines those according to a more fundamental set of laws (like the laws of muscle composition, organic chemistry, chemistry, newtonian physics, quantum physics as these all apply for a person throwing a right hook), they’re determined arbitrarily by the designer/animator and have none of those underlying rules operating behind them.