Source : Free On-Line Dictionary of Computing

back-propagation
     
        (Or "backpropagation") A learning {algorithm} for modifying a
        {feed-forward} {neural network} which minimises a continuous
        "{error function}" or "{objective function}."
        Back-propagation is a "{gradient descent}" method of training
        in that it uses gradient information to modify the network
        weights to decrease the value of the error function on
        subsequent tests of the inputs.  Other gradient-based methods
        from {numerical analysis} can be used to train networks more
        efficiently.
     
        Back-propagation makes use of a mathematical trick when the
        network is simulated on a digital computer, yielding in just
        two traversals of the network (once forward, and once back)
        both the difference between the desired and actual output, and
        the derivatives of this difference with respect to the
        connection weights.