An admission is something that a party to the action has said that is later introduced as evidence against him or her. For example, Frank is standing outside of a house holding a television set. When confronted by the police; he says “I stole the T.V.” Later at his burglary trial, the prosecution offers Frank's statement about stealing the television (an admission) as proof of his guilt.
Admissions are generally allowed into evidence even if they are hearsay because the party against whom the admission is being offered has the opportunity to explain the statement or refute the statement. (Hearsay is a second-hand statement offered in court as evidence of what was actually said. Hearsay is not allowed as evidence, unless some exception to the hearsay rule applies.) In a civil case, a Request for Admissions is a pleading served on an opposing party. If the opposing party does not deny the admission, it is generally considered true and cannot be contested.