na-adjective
Describes a child or pet that is calm, follows rules, and does not cause trouble. Often used in the negative form きすぐじゃない to mean 'naughty' or 'misbehaving'.
今日は子供たちがきすぐにしている。
The children are being well-behaved today.
この犬はとてもきすぐで、言うことをよく聞く。
This dog is very obedient and listens well.
おとなしい means 'quiet, gentle, docile' and focuses on a calm, unobtrusive nature. きすぐ emphasizes active obedience and good behavior, often in contrast to being naughty.
行儀がいい is a phrase meaning 'well-mannered' or 'polite', often used for behavior at the table or in formal settings. きすぐ is a simpler, more colloquial term for general good behavior.
The origin is uncertain. The kanji 生 (pure, raw) and 直 (straight, direct) may suggest an original meaning of 'straightforward and unspoiled', but the word is now used almost exclusively in kana.