An emergent algorithm is a way of teaching computers, or computers teaching themselves, how to do something without actually giving them specific instructions. It's like if you were teaching a baby how to talk. You wouldn't start by telling them the English alphabet, or how to make all the different words and grammar. You'd just point at things and make noises, and the baby would learn things by listening to you and trying things out, over time learning how to communicate. Emergent algorithms work in a similar way. The computer starts off with very little information, but by looking at its environment and experimenting with different things, over time it can 'learn' a set of instructions or rules it can then use to do something very specific.