Feed-forward neural networks:
The signals in a feedforward network flow in one direction, from input, through successive hidden layers, to the output.
The connections between the nodes do not form a cycle as such, it is different from recurrent neural networks.
Backpropagation is a training algorithm consisting of 2 steps:
Feedforward the values.
Calculate the error and propagate it back to the earlier layers.
Forward-propagation is a part of the backpropagation algorithm but comes before back-propagating the signals from the nodes. The basic type of neural network is a multi-layer perceptron, which is a Feed-forward backpropagation neural network.
Hope this answer helps.