What does it mean when the model Learning Curve displays this behavior?
Yes, this is overfitting. As you can see in your loss curve the training loss is steadily decreasing like it should, but at the same time your validiation loss is increasing. On data the model hasn't seen before it's actually getting worse!
This means your model is starting to learn the training data, and does not instead keep the learning generalized. As soon as validation loss is increasing you should stop training.
I'm answering this question although overfitting is a general concept and has been answered before because this question might want to have an answer that is specific to LSTMs.