There has been many conjectures as to the subject and the plot. Well, if you want a good hint, let me give you a precious one: read the novella "La Jalousie" (Jealousy, 1957), by Alain Robbe-Grillet, who is also the screenwriter of "Marienbad". "La Jalousie" is the thematic and "ideological" inspiration for "Marienbad".
Robbe-Grillet (one of the top names of the French "Nouveau Roman" movement along with Nathalie Sarraute, Marguerite Duras, Michel Butor, etc), was a former agronomist/ mathematician (and his writing shows it) who became a writer/filmmaker with a very personal, geometrical, unemotional, descriptive style. The novella "La Jalousie", like most Nouveau Roman books, is essentially cinematic in their approach of characters and plot, functioning like a film camera, a non-opinionated unobtrusive observer, but insightfully revealing in its "detachment".
His novella "La Jalousie" is a fascinating, maze-like circular construction, in which beginning and end mingle many times over, each time from a different perspective, just like observing a house or a sculpture from different angles one at a time -- which means each angle is only partially accurate, revealing but a portion of the truth, while hiding another. The "observer/narrator" in the book (the husband, but written in the third person - "he") tries to locate in PLACE and TIME the precise moment in which the feeling of jealousy arises in him as he tries to find the extent of his wife's relationship with another man (a.k.a. the threesome in the film). Did an affair really happen? Is it yet going to happen? Or is it his imagination, his suspicion, just his jealous feeling? (btw, this is the same theme as Proust's incomparable masterpiece "La Prisonnière", treated in antipodal, totally psychological, but equally obsessive style).
As in most "Nouveau Roman" novels, the notion of TIME in "La Jalousie" (and also in "Marienbad") is transformed and deformed; the approach of the characters is non-psychological, meaning that thoughts and outbursts of emotion are not dealt with, only the description of places, words, gestures and actions. Everything (even a very strong feeling like the birth of jealousy) is apprehended only through the observation of external facts: small gestures, the position of a chair or a table, a glass found full or empty, an unexpected sound, the way the woman combs her hair or looks at herself in the mirror, a suddenly unusual way of getting up or sitting down which leads to the husband's perception that something has suddenly, dangerously, definitely changed.
Well, it made very much sense to me that language-experimentalist book-worm Alain Resnais (think of all of his movies which were based on literature) and his fascination with memory and the brain (think "Hiroshima Mon Amour", "Je t'Aime Je t'Aime" and "Mon Oncle d'Amérique") should venture in constructing this film in visual terms using the geometrical structure of the novel (hence the breathtaking serpentine camera movements), with no beginning or end, respecting its "external", non-psychological, non-motivational approach of the characters and the plot, never condescending to "explanations".
See the film and read the book! I'm sure that, if you've liked (or been baffled by) the film on a first viewing, you'll have many insights on a second viewing of this absorbing, totally fascinating movie after reading the book on which it is structurally/esthetically based. While it's not essential to do so, it could be kind of a bonus! What else can I say? A definitive, revolutionary, undisputed film classic - 10/10