Backpropagation is an algorithm used for training artificial neural networks. It is a supervised learning technique that helps adjust the weights of the network to minimize the difference between the predicted outputs and the actual target outputs. The term "backpropagation" is short for "backward propagation of errors," signifying its two-step process: forward pass and backward pass.
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Backpropagation applies the chain rule from a neural network's output toward its input to compute the gradient of a loss with respect to every parameter.
What is backpropagation really doing? by 3Blue1Brown (2017)
Source. Good hand-wave intuition, but does not describe the exact algorithm.