A fundamental algorithm in neural network training, serving to fine-tune the weights of the network to minimize errors. It operates by calculating the gradient of the loss function (which measures the difference between the predicted and actual outputs) with respect to each weight in the network, using the chain rule of calculus. This process involves two main phases: a forward pass, where input data is passed through the network to obtain a prediction, and a backward pass, where gradients are propagated back through the network to update the weights. This iterative adjustment of weights allows the network to learn from the data, improving its accuracy over time. Backpropagation is crucial for the development of deep learning models, enabling them to learn complex patterns in large datasets.