The method for working out which of a model’s millions of internal settings were responsible for a mistake. The model makes a prediction, the error is measured, and that error is then traced backwards through the layers so each setting can be nudged by the right amount in the right direction. Without a way to assign blame across so many numbers, training a large network would be impossible.
Technical view
It is an efficient application of the chain rule from calculus, computing the gradient of the loss with respect to every parameter in roughly the same time as a single forward pass. This efficiency is the whole point; a naive approach would be hopelessly slow. In practice it is handled by automatic differentiation built into frameworks such as PyTorch, so practitioners rarely implement it directly, but understanding it explains most of why models train the way they do.
Related
Part of AI Terminology Index, section: How the Machinery Works.