Backpropagation
Backpropagation is the method used to train neural networks. After the network makes a guess, the program measures the error and works backward through the layers, calculating how much each weight contributed to it, then nudges every weight slightly in the direction that reduces the error. Repeating this over many examples is how a network learns.
Why it comes up
A 1986 Nature paper by Rumelhart, Hinton and Williams made backpropagation the standard way to train multi-layer networks; earlier versions existed, and Hinton has since said he doubts the brain learns this way.
Geoffrey Hinton
Yann LeCun