A statement made by a person suspected or charged with a crime, that he (or she) did, in fact, commit that crime.
In R v Lambe, a 1791 English case published at 2 Leach 552:
"The general rule ... is, that a free and voluntary confession made by a person accused of an offence is receivable in evidence against him, ... as the highest and most satisfactory proof of guilt, because it is fairly presumed that no man would make such a confession against himself, if the facts confessed were not true."
Modern criminal law now require that a confession may not be admissible failing evidence that it was preceded by a warning to the accused such as, in the USA, the Miranda warning.