Why is my training loss much higher than my testing loss?

A Keras model has two modes: training and testing. Regularization mechanisms, such as Dropout and L1/L2 weight regularization, are turned off at testing time. They are reflected in the training time loss but not in the test time loss.

Besides, the training loss that Keras displays is the average of the losses for each batch of training data, over the current epoch. Because your model is changing over time, the loss over the first batches of an epoch is generally higher than over the last batches. This can bring the epoch-wise average down. On the other hand, the testing loss for an epoch is computed using the model as it is at the end of the epoch, resulting in a lower loss.