Backpropagation is the basis for training a supervised neural network. Static backpropagation is used to produce an instantaneous mapping of a static (time independent) input to a static output. These networks are used to solve static classification problems such as optical character recognition (OCR).
At the core of all backpropagation methods is an application of the chain rule for ordered partial derivatives to calculate the sensitivity that a cost function has with respect to the internal states and weights of a network. In other words, the term backpropagation is used to imply a backward pass of error to each internal node within the network, which is then used to calculate weight gradients for that node. Learning progresses by alternately propagating forward the activations and propagating backward the instantaneous errors.