Well-mannered means polite in the way you speak and behave — saying please and thank you, letting others go first, not interrupting, knowing what to do at a table. It is about learned social behaviour, not about being a good person underneath; a cold, selfish person can be perfectly well-mannered, and that gap is sometimes exactly what a writer wants you to notice. The word is used most about children, because manners are something children are taught, and a Taiwanese student will meet it constantly in that context: "such a well-mannered boy". Adults get it too, usually with a slightly old-fashioned or approving air. It is also used about animals, particularly dogs and horses, meaning well-trained and calm around people. It sits before a noun or after be, and takes more/most. Its opposite, bad-mannered or ill-mannered, is used less than you would expect — English usually says rude. Note that well-mannered praises how someone behaves, while well-behaved praises that they caused no trouble, and polite is the plain everyday word that covers both.