The Processing Power: it is more expensive than you think and effective methods are as a pay per use system such as the one by google or machines (as made by NVIDIA for example) which adds up to the Graphic Processing units (GPU) that imaging requires.
More prosaically there are terms which are of use when assessing speed:
Epoch: This is the process of processing all the data through the artificial neural network, from the input layer to the output layer through the hidden layer.
Learning rate: It is the number of times epochs are passed through the neural layer divided by time. The higher the learning rate the more precise it becomes, however, the more it consumes computing power, however both too high and too low learning rates are a waste of time and resource.