Its a hearing where the verdict (guilty) is not in dispute but there are factual circumstances that may affect the sentence. New Judge gave an excellent example yesterday.
Defendant is in court for speeding. Does not deny that they were speeding but says that they were not doing the 120 alleged by the police but were only doing 80 and are offering evidence to support this. The two speeds carry different punishments so a Newton hearing can be held to establish the facts.
A Newton hearing or inquiry is a comparatively modern legal procedure in English law, used where the two sides offer such conflicting evidence that a judge sitting alone (that is, without a jury) tries to ascertain which party is telling the truth.
And just to add that Newton Hearings are also held in Magistrates' Courts for matters which are being heard there. The Magistrates (or District Judge (Magistrates' Court)) hear the matter and make the decision.