(covers information from several alternate timelines)
Cetacean Ops was the facility aboard various Starfleet starships, during the latter half of the 24th century, which was responsible for ship's navigation. They generally contained an aquarium, so as to simulate the natural habitat of cetaceans.
In 2366 of an alternate timeline created by a time traveling USS Enterprise-C, Doctor Joshua Kim was ordered to report to Cetacean Ops on the USS Enterprise-D, shortly after the Galaxy-class warship encountered a temporal rift. (TNG: "Yesterday's Enterprise")
The term "Cetacean Ops" was only heard in the "background chatter" during "Yesterday's Enterprise". The subtitles for the episode on streaming services – including both Netflix and Amazon – as well as the TNG Season 3 Blu-ray release, give the facility's name as "station Ops." A line in "The Perfect Mate", in which Geordi La Forge mentions "dolphins" on board, may have alluded to the existence of the facility. However, it wasn't until Star Trek: Lower Decks that it was established that Cetacean Ops also existed in the regular timeline.
According to the 1996 reference book Star Trek: The Next Generation USS Enterprise NCC-1701-D Blueprints, the cetacean ops facilities, including a cetacean navigation lab and four cetacean lifeboats, were located on Deck 13, with the navigation labs extending into Deck 14 as well.  Conceptual artwork at Andrew Probert's website shows that the facility may have been featured in the original version of Star Trek Online.
According to the Star Trek: The Next Generation Technical Manual, the ship's dolphins work in navigation and are overseen by two whales of species Orcinus orca takayai, or Takaya's Whales. This references the 1988 anime OVA Gunbuster, where the starship Exelion uses dolphins for navigation due to their natural familiarity with moving in three dimensions; as well as the name of that series' protagonist, Noriko Takaya.