A well-spoken person speaks clearly, politely, and in a way that other people judge to be correct — good grammar, a careful choice of words, an accent that sounds educated. You hear it in a job reference, in a description of someone's grown-up child, in a news report about a witness: a quiet, well-spoken young man.

Now the part your dictionary may not tell you. Read those words again — 'in a way that is considered correct'. Considered by whom? This word carries a class judgement inside it, especially in Britain. To call someone well-spoken is very often to say that they sound middle-class or upper-class; that they do not have a strong regional or working-class accent. So it praises the speaker while quietly measuring them against one particular way of speaking. Plenty of British people now find it a slightly uncomfortable word for exactly that reason, and some use it with a raised eyebrow.

You will also notice where it tends to appear. It is used a lot about someone whom the speaker did not expect to speak that way — a young person, a poor person, a foreigner, someone recently arrested. 'He was very well-spoken' after a crime story is doing real work: it means he did not sound like the sort of person we expected. That is worth seeing clearly.

As a compliment to someone's face it is warm and safe enough: your daughter is so well-spoken. In American English it is used more loosely, closer to 'articulate' — good at expressing themselves — with less of the accent question attached, though 'articulate' has its own troubles there.