How machines learn
Backpropagation is the algorithm that works out how much each weight in a neural network contributed to an error, so every weight can be adjusted correctly.
A neural network has millions of adjustable numbers spread across many layers. When its final answer is wrong, which numbers deserve the blame? Backpropagation answers that. It starts at the output, measures the error, and passes blame backwards layer by layer, sharing it out to every weight along the way.
The trick is a rule from calculus that lets the blame be computed layer by layer without redoing work. The result is a gradient: for each weight, a number saying which direction would reduce the error. Gradient descent then uses those numbers to take a small step. Together they form the training loop.
Backpropagation was popularized in 1986 and is still the workhorse of deep learning. It is purely mechanical; the network is not 'reflecting' on its mistakes. Without it, training deep networks would be hopelessly slow, which is partly why neural networks stalled for decades.
After a lost match, a coach reviews the tape backwards from the final goal to see which earlier passes went wrong; backpropagation does this for a network's mistakes.