Synaptic potentials
The measurement of synaptic potentials was an indication of brain activity, the level of the synaptic potentials being related to the state (healthy or otherwise) of a person's neural patterns.

In 2373, Benjamin Sisko suffered odd synaptic potentials following an accident in which he was exposed to a plasma burst from a holosuite console. The condition was associated with temporary post-neural shock syndrome, and coincided with a series of visions that Sisko experienced concerning the future of Bajor. The condition deteriorated, resulting in painful and crippling headaches. Doctor Bashir determined that his basal ganglia were starting to depolarize and, later, that his entire central nervous system was depolarizing, at which point the condition had become life threatening. Eventually, it was necessary to perform a neuropolaric induction to save Sisko's life; this was a success, returning his brain activity to normal, but it also put an end to the visions. ()

Sisko suffered again from unusual synaptic potentials in 2374 in association with another vision, this time of the past. On this occasion, his neural pathways returned to normal without the need for surgery after the vision concluded. ()

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Background information
In , the phrase "synaptic potentials" was a form of technobabble  used as an indication that Benjamin Sisko was experiencing visions, most likely associated with or caused by the Prophets.

In real world neuroscience, a synapse is the junction between two neurons (nerve cells) in the central nervous system (the brain and spinal cord). Nerve impulses are transmitted across a synapse when the presynaptic neuron releases neurotransmitter that causes a change in electrical state (specifically, a depolarization) of the postsynaptic neuron. The depolarization of the postsynaptic cell is referred to as a "synaptic potential". 

The association of odd synaptic potentials with post-neural shock syndrome is plausible. It is clear in  that the "odd" synaptic potentials experienced by Sisko are associated with depolarization, which in real world neuroscience would mean that the postsynaptic neurons would require less stimulation to be excited and conduct nerve impulses . Hence, they would be more active than usual, rendering the patient more sensitive to stimuli.

de:Synaptisches Potential
Biology