problems during training a MLP type of network
When the training loss is lower than the validation loss, the model is said to overfit the training data, i.e. it has learned so much from the training data that it only adjusts well to it and it can't generalize to new data. This phenomena is regarded as the variance of the model. The bias of the model is the difference between the training loss and and the loss you've previoussly selected as the minimum loss reachable, or the desired one. 

However, this analysts is usually done over other well known metrics, such as precision and recall. You first calculate these metrics on your training data, and then, on the evaluation data. Then you perform the analysis taking the same considerations.

In order to reduce the variance/overfitting, there are common techniques:


Increse the training data by adding more instances, if available
If no more instances are available, perform data augmentation to increase the training dataset
Use regularization, for example, dropout.
Shorten the network. If there are lots of layers, the network may be learning too specific features from the training data 


As mentioned before, I'd perform the analysis using other metrics rather than the loss.