(covers information from several alternate timelines)
Uhura holding a purring tribble
A purr was a guttural vocalization made by various types of animals, often used by humanoids as an onomatopoeia. It was often done as an indication of pleasure or happiness. (TAS: "The Terratin Incident"; TNG: "Schisms")
In 2259 of the alternate reality, Montgomery Scott assured Captain James T. Kirk that USS Enterprise's warp core was "purring like a kitten" (i.e. running well). (Star Trek Into Darkness)
In 2268, Nyota Uhura was delighted when the tribble she held began to purr. Cyrano Jones assured her that it meant the tribble liked her. (TOS: "The Trouble with Tribbles")
Cats were well-known for their purring, particularly when petted. In his poem Ode to Spot, Data referred to this sound as "a singular development of cat communications". (TNG: "Schisms") Reginald Barclay's cat Neelix also purred. According to Deanna Troi, this trait probably influenced Barclay's decision to make a holographic re-creation of the actual Neelix purr. (VOY: "Life Line") Montgomery Scott and Miles O'Brien both compared starship engines to kittens purring; Scott in 2269 (USS Enterprise), and O'Brien in 2370 (USS Prometheus). (TAS: "The Terratin Incident"; DS9: "Second Sight")
Caitians often purred when they spoke. (Star Trek: The Animated Series)
Guinan's imaginary friend, a Tarcassian razor beast, had "the softest purr you'd ever heard." (TNG: "Imaginary Friend")
In 3188, Cleveland Booker's cat Grudge was purring as he and Michael Burnham were talking. (DIS: "That Hope Is You, Part 1")
The closed captioning for this episode identified the vocalization.