This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
(covers information from several alternate timelines)
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")
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 recreation 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")