Explain the concept of a neural network's backpropagation algorithm and its significance in training deep learning models.

The backpropagation algorithm is essential for training neural networks by minimizing the error between predicted and actual outputs. It involves forward propagation to calculate the output and backward propagation to compute the gradient of the loss function concerning each weight. By iteratively updating weights using gradient descent, backpropagation optimizes the network parameters, enabling deep learning models to learn complex patterns and representations from data.