There are many parameters that can cause a neural network to stop training.
As you may know, an epoch is the full pass of the training algorithm over the entire training set. In general, the training will stop before reaching the specified maximum number of epochs to avoid overfitting to the data, thus improving the network generalization. That is, the training will stop if the results of the cross validation are not getting any better (within some tolerance).
Please refer to the following link for more information on the early stopping behavior to improving generalization of the network:
