As far as I can tell, the term "gaslighting" didn't come into common usage until the 60s. But this is the origin, this and the play on which it is based. (There was an earlier British film of the play, as well.) Perhaps when the play was written, the idea was that one person was being "gaslit", but in more recent years, it feels more like a communal problem.
The key isn't just that "Gregory" (Charles Boyer) is manipulating his wife Paula (Ingrid Bergman) into thinking she is going insane. It's also that he keeps Paula separated from the outside world. She never has anyone else to offer other interpretations of events ... she must rely only on herself, and Gregory, who of course can't be trusted. She is saved by a Scotland Yard Inspector (Joseph Cotten) whose interest in the case is rather hokey. He convinces Paula that she is not insane, that her perceptions are accurate, setting up a final scene when Paula confronts Gregory (real name Sergius) and plays a bit of psychological abuse on him.
It would have been nice for Paula to figure things out on her own ... the fact that another man has to save the day doesn't make Gaslight a model of female empowerment. But Cukor and the writers are always more interested in maintaining a creepy suspense than in making an airtight plot. The inspiration for Gregory's chicanery (he's after missing jewels) is confusing if you try too hard to fit it into the film's timeline, and the Inspector's presence is especially obvious for existing primarily as a plot device. Nonetheless, Gaslight works, both as a kind of horror story and as a noir ... it's as fun to watch now as it was in 1944.
Gaslight was nominated for seven Oscars, winning for Best Art Direction-Interior Decoration, Black-and-White (among the other nominees in that category were Laura and Since You Went Away). It was also nominated in many of the major categories (Best Picture, Actor, Supporting Actress, Screenplay, and Black & White Cinematography), while Bergman took home the Oscar for her performance, besting the likes of Bette Davis and Barbara Stanwyck. One never knows exactly how the relationship between a director and an actor affects what we see on screen, but Gaslight takes full advantage of the ways Bergman can seem so emotionally committed to a role. Angela Lansbury, who got the Supporting Actress nomination, was making her film debut.
Gaslight doesn't disappoint, and its resonance with our times adds value.