In David Lynch's groundbreaking TV series Twin Peaks, the ancient cultural convention of using owls as symbols for the supernatural, bad omens, and harbingers of death is leveraged heavily through both imagery and plot elements. The message "The owls are not what they seem" was first delivered to Special Agent Dale Cooper by the Giant (actor Carel Struycken), who visited him in a dream while he slept in his room at the Great Northern hotel. This scene appeared in the episode appropriately titled "May The Giant Be With You" (Episode 8) that originally aired on September 30, 1990.
Considered by many to be among the most memorable scenes from the series, this quote is sometimes mistaken as belonging to to a scene that was in another episode ("Zen, or the Skill to Catch a Killer", Episode 2, originally airing April 19, 1990). This scene, probably the most jarring one of the first season, is the one containing the backwards-talking dancing midget, referred to in the series as "The Man From Another Place" and played by actor Michael J. Anderson. The dream sequence from the end of this episode is far more amazing than the Owls scene in the Giant episode; in it, the dwarf reveals to Cooper: "That gum you like is going to come back in style." He introduces Laura Palmer to Cooper in the dream ("She's my cousin... but doesn't she look... almost exactly like Laura Palmer?"), and she whispers in Cooper's ear the name of her killer, which Cooper can not seem to remember upon waking. This scene was very surreal and made a lot of viewers freak out because it was quite unlike anything that had ever been seen in a prime-time TV series before.
"The owls are not what they seem" was also a message delivered to Agent Cooper by Major Garland Briggs (actor Don S. Davis) in the episode entitled "Coma" (Episode 9, originally airing October 6, 1990). Briggs works for the United States Air Force in charge of a unit operating deep space monitors (possibly an allusion to Project Blue Book), and received the message along with the word "Cooper" repeated three times, from the military's radio telescopes. We learn later in the series that the monitors are actually pointed at the woods near Twin Peaks.
Many theories have been developed over the years to explain exactly what this message means. If the owls are not what they seem, what are they? Interpretations have included aliens or alien abductees, the killer "BOB" or other dugpas, servants of the lodges (the Black Lodge and/or White Lodge) or Native American spirits, demons, angels, or surveillance devices. In Episode 24, the Log Lady reveals that she heard the same owl call on the night her husband died as she did on the night Laura Palmer died, and remarks to Agent Cooper in Episode 5 that "The owls won't see us in here" after they enter her cabin, later describing the events of the latter night with "the owls were flying" and "the owls were near".
In one interview given in 2019, David Lynch suggested that the owls were a reference to the mascot of Temple University in Philadelphia, Pennsylvania where he once lived. "Back when I was living on Aspen Street," Lynch explained, "I used to look out our rear window at the lights from Temple a few blocks to the northeast. It seemed like another world, a place both wonderful and strange when compared to the sick, twisted, violent, fear-ridden, decadent, decaying neighborhood where Peggy and I lived at the time."
Complete transcripts of the cited episodes can be found here:
http://www.glastonberrygrove.net/texts/episode2.html
http://www.glastonberrygrove.net/texts/episode5.html
http://www.glastonberrygrove.net/texts/episode8.html
http://www.glastonberrygrove.net/texts/episode24.html
An attempt to catalog the visual appearance of owls in the series can be found here:
https://twinpeaksblog.com/2020/02/02/all-in-the-details-the-owls-of-twin-peaks/