Most generally, this means to "increase the effect of", or "increase the effectiveness of".

In biological neural networks, this refers to a synapse becoming more effective in its ability to excite, or inhibit the firing of its neuron in response to an incoming signal (in biological terms, a signal is called an action potential). Potentiation is the opposite of Depression.

This is sometimes used as a close synonym in Netlab. It can refer to increasing the strength of a connection weight by making it more positive (if it is an excitatory synapse), or more negative (if it is an inhibitory synapse). That is, increasing the absolute value of a connection weight in Netlab (whether it is negative or positive), is analogous to potentiation in biology.