Acceptable means good enough to say yes to. Not brilliant, not a disaster — just past the line where someone will agree. A hotel room that is small but clean, a price you would rather not pay but will, a C on the exam.
It nearly always takes TO when you name the person judging: an offer acceptable to both sides. A second use is about manners and rules rather than quality — socially acceptable behaviour is behaviour nobody objects to, and 'that language is not acceptable here' is a warning, not a review. The opposite, unacceptable, hits far harder than acceptable is warm: calling someone's work acceptable is faint praise, calling it unacceptable is a complaint. Do not mix it up with accepted — an acceptable excuse is one that could be taken, an accepted excuse is one that was. And 'perfectly acceptable' is the phrase people reach for when they are defending something ordinary.
1adjectiveacceptableGood enough to be agreed to or allowed.
“The offer was acceptable to both sides, so the meeting ended early.”
synonyms: satisfactory, adequate, tolerable
2adjectivepermissibleAllowed by the rules, or by what the people around you think is right.
“Shouting at a referee is not acceptable behaviour, whatever the score.”
synonyms: permissible, appropriate
Acceptable came through Middle French from Latin acceptābilis, 'worthy of acceptance'. Underneath the long word is plain construction: accept plus -able, 'able to be accepted', the same recipe as readable and washable. The trail runs back further still, to the Proto-Indo-European root *kap-.
Proto-Indo-European
*kap-
Latin
acceptābilis — worthy of acceptance
Middle French
acceptable
Middle English
acceptable
English, today
acceptable
From Middle English acceptable, from Anglo-Norman - and Middle French acceptable, from Latin acceptābilis (“worthy of acceptance”). Morphologically accept + -able.
Etymology from Wiktionary, CC BY-SA