Long short-term memory. A neural network (NN) architecture that contains recurrent NN blocks that can remember a value for an arbitrary length of time. A very popular building block for deep NN.
Long short-term memory neural networks (LSTMs) are a subset of recurrent neural networks. They can take time-series data and make predictions using knowledge of how the system is evolving.
A major benefit to LSTMs is their ability to store and utilize long-term information, not just what they are provided at a particular instance. For more information on LSTMs check out these links from colah's blog post and MachineLearningMastery.