A hurricane or typhoon was a type of violent storm that forms over the warm water of Earth's oceans. Once it made landfall, it lost power and dissipated back into the atmosphere. Hurricanes were known to produce wind speeds of over 74 mph (118 kph), and among other things, tornadoes, and torrential rain. As hurricanes were cyclonic by nature, at the center of the circulation there was the area that contained the lowest atmospheric pressure and relative calm known as the "eye".
In a conversation with Kathryn Janeway, the Leonardo da Vinci hologram asked her how she came to the Americas, she replied that it was "a long story," but that it involved "a Portuguese ship, some Turkish pirates, [and] a couple of hurricanes." (VOY: "Concerning Flight")
During the 19th century, a sailing ship commanded by British Royal Navy Captain Cray was hit by a typhoon in the Pacific Ocean. While the ship sustained heavy damage in the storm, Cray and his crew were able to go against all odds, and arrive back in London eight months later in the tattered remains of his ship. (VOY: "Year of Hell")
While camping on Archer IV in 2151, the landing party from the Enterprise encountered a storm front, with gusting winds approaching 80 kph. Charles Tucker, a Florida native, thought nothing of it, "compared to a hurricane coming up through the Florida Keys." (ENT: "Strange New World")
In 2032, after becoming trapped inside a graviton ellipse aboard Ares IV, Earth astronaut John Kelly described the interior of the ellipse as being "very calm, like [he was] in the eye of a hurricane." (VOY: "One Small Step")
In the early 23rd century, when Gen Rhys was five years old, a hurricane wiped out his town. He later noted that he owed his life to the Starfleet crew that managed the evacuations. (DIS: "The Examples")
In 2365, William T. Riker compared being in the breathable zone, found on Theta VIII, that was surrounded by ammonia storms located less than a kilometer away, to being in the eye of a hurricane. (TNG: "The Royale")