Drowning was a condition where an individual's lungs were filled with something other than what they normally breathed. It could eventually lead to death.
In 2151, the Novan Akary was in danger to drown in an underground well on Terra Nova. (ENT: "Terra Nova")
In 2269, James T. Kirk, Leonard McCoy and Carver nearly drowned when the urn, constructed on the Taurean planet, they were hiding in filled with rain water. (TAS: "The Lorelei Signal")
Also in 2269, Spock and Kirk were saved from drowning by the Aquans and turned into water breathers. (TAS: "The Ambergris Element")
Later that year, Nurse Chapel nearly drowned in a fish tank due to her reduced size. (TAS: "The Terratin Incident")
In 2358, Vice Admiral Janeway drowned under the polar ice cap on Tau Ceti Prime. (VOY: "Coda")
In 2336, young Kestra Troi drowned, an event which traumatized Lwaxana Troi for years. (TNG: "Dark Page")
In 2370, Bajoran collaborator Ches'sarro Seeto was drowned in a pond on his property after Odo began questioning Vaatrik Pallra about his identity. (DS9: "Necessary Evil")
The Joranian ostrich could sometimes hold its head under water for so long that it drowned. (DS9: "Past Prologue")
In 2381 on the USS Cerritos, Ensign Brad Boimler nearly drowned in Cetacean Ops, but he was rescued by Lieutenants junior grade Kimolu and Matt. (LD: "First First Contact")
The term could also refer to drinking alcoholic beverages for comfort. In 2257, Sylvia Tilly, while venting her frustration in the USS Discovery's sickbay, remarked that, if none of her options ultimately succeeded, she should "try drowning [her] ineptitude in a Risan mai-tai." (DIS: "New Eden")