If you learn about machine learning you will stumble over three terms that are related:
- Gradient descent,
- the Delta rule and
Gradient descent is a way to find a minimum in a high-dimensional space. You go in direction of the steepest descent.
The delta rule is an update rule for single layer perceptrons. It makes use of gradient descent.
Backpropagation is an efficient implementation of gradient descent, where a rule can be formulated which has some recursively defined parts. Those parts belong to neurons of different layers and get calculated from the output-layer (last layer) to the first hidden layer.