To recant is to say publicly that you no longer hold a belief you once held and stated — usually a religious or political one, and usually because you are under pressure to give it up. That pressure is really part of the word. History is where you meet it: people were made to recant their faith in front of a court, on pain of death. Galileo recanted. Anyone who has read about the Reformation or the Inquisition has met this word.

So it carries a shadow. To recant is not simply to change your mind — that is 'reconsider' or 'change your view'. It is to stand up and take back what you said, publicly, often against your own heart. A person who recants may still privately believe the thing.

It has stretched, carefully, to modern uses: a witness recants their testimony (says the evidence they gave was false), a scientist recants a claim, a politician recants a promise. In law, 'recant' about testimony is a standard term. Outside of these, it stays formal and rather literary; in everyday English people 'take it back' or 'go back on what they said'.