It's been a while since I've seen Belle de Jour, but hopefully my memory can do it justice. The cat stuff seems to come from a combination of factors:
First, as Roger Ebert suggests in his review of the film, Severine has lots of little, mundane fetishes that trigger her grandiose, kinky fantasies. As Ebert says:
Severine is a masochist who likes to be handled roughly, but she also
has various little turn-ons that the movie wisely never explains,
because they are hers alone. The mewling of cats, for example, and the
sound of a certain kind of carriage bell. These sounds accompany the
film's famous fantasy scenes, including the opening in which she rides
with Pierre out to the country, where he orders two carriage drivers
to assault her.
These mundane sounds and images provide a transition into/out of Severine's fantasies. If I recall correctly, these visual and audio cues are actually used at the end of the film as a method to call into question how much of it is real and how much is part of Severine's fantasy world, though don't quote me on that bit.
Second, cats are often thought of as a symbol of feminine sexiness and sexuality. Director Luis Bunuel could have easily decided that one of Severine's little turn-ons would be dogs, and give the mansion owner a bunch of little shih tzus or corgis instead of cats. But the cats seem to emphasize that this movie - Severine's fantasies, her involvement with the brothel, etc. - is about Severine's sexuality and autonomy, nobody else's. (Indeed, as Ebert suggests in his review, Severine's kinks seem to be very much about her, rather than any potential partner - even her husband.)
And third, as mentioned before, the director is Luis Bunuel, who is probably most famous for his collaboration with Salvador Dali that produced Un Chien Andalou (fair warning to anybody who isn't already familiar: there are some rather violent/graphic scenes in the video).
(Fun fact: As you can kinda tell from the preview image that the imdb page shows on the trailer, the razor-to-the-eye shot was actually filmed using a dead cow - or possibly donkey? - rather than an actual person.)
But anyway, the point is that "presenting the audience with weird mysteries (often packaged in mundane things like cats or domestic squabbles) and never fully explaining them" is a Luis Bunuel trademark. I often find his work to be somewhat akin to existentialist theater like Eugene Ionesco's Cantatrice Chauve (or Bald Soprano), in which a random, otherwise mundane phrase like "It's not that way, it's over here" makes up an important part of the story. Despite not being a particularly out-of-the-ordinary phrase in and of itself, it becomes (intentionally) strange and confusing by the sheer lack of explanation that surrounds it. (This seemingly innocuous phrase in Bald Soprano feels that much more odd because it comes directly after the characters spit out a bunch of phrases that are much more obvious nonsense - much in the same way that the cats and the meowing in Belle de Jour stand out as much as they do because they are so innocuous/mundane when placed next to Severine's fantasies about being whipped and having mud slung at her.)