Long-term potentiation is a form of neuronal plasticity, which may form the biological basis for some kinds of memory.

In brief, long-term potentiation refers to the fact that if two neurons are active at the same time, the connection between them may be strengthened. This change ("potentiation") can last for minutes to hours. This may serve to lay a foundation for more permanent changes, such as the construction of new connections (synapses) between the neurons.

Further reading: L. Squire and E. Kandel (2000). Memory: From Mind to Molecules. New York: Scientific American Library.