1a: an acutely painful or embarrassing misunderstanding
b: scandal
c: a violently confused or bitterly complicated altercation
d: an intricate or complicated situation (as in a drama or novel)
2: a confused mass
Imbroglio and "embroilment" are more than just synonyms; they're also linked through etymology. Both descend from the Middle French verb embrouiller (same meaning as "embroil"), from the prefix em-, meaning "thoroughly," plus brouiller, meaning "to mix" or "to confuse." ("Brouiller" is itself a descendant of an Old French word for broth.) Early in the 17th century, English speakers began using "embroil," a direct adaptation of "embrouiller." Our noun "embroilment," which also entered the language in the early 17th century, comes from the same source. Meanwhile, the Italians were using their own alteration of "embrouiller" : imbrogliare, meaning "to entangle." In the mid-18th century, English speakers embraced the Italian noun imbroglio as well.
From Vocabulary.com:
an intricate and confusing interpersonal or political situation