(covers information from several alternate timelines)
A lightning storm was a meteorological phenomenon characterized by a high amount of electrical activity.
When Wesley Crusher was testing himself in preparation for his psych test for the Starfleet Academy entrance requirements, he asked Worf's opinion as to what fears he could face. "Lightning storms" was one of the ideas Wesley thought of. (TNG: "Coming of Age")
After hearing Pavel Chekov describe an anomaly as a "lightning storm in space", James T. Kirk immediately recognized it as the same phenomenon that preceded Nero's earlier incursion which had killed his father. (Star Trek)