It's something that was invented for chess but can apply to many other competitive games (magic the gathering had it...more on that in a bit). Essentially if you play a superior opponent and win it goes up significantly, but if you loose his doesn't go up much if at all (I could be off on this). Seems like a great system, but the problem with it is two fold. First there are those that would get high elo and then not play and keep it high (which is why wizards of the coast changed to their own system for magic the gathering). Also it can be fair easy to farm it especially in destiny. It is a wildly inadequate system for destiny and in no way portrays a players skill. Besides that the two sites I know of that track the elo don't match up anyways. All in all it's just something for those concerned with k/d to brag about and is basically mostly pointless. Although I guess k/d is more important in destiny than in most games as the game modes are basically tdm with some side objectives.