1) to state something is true in answering a complaint filed in a lawsuit the defendant will admit or deny each allegation in his or her answer filed with the court. If he or she agrees and states that he/she did what he/she is accused of, then the allegation need not be proved in trial.

2) in criminal law, to agree a fact is true or confess guilt. 

3) to allow as evidence in a trial, as the judge says: "Exhiibit D, the letter, is admitted..But an admission cannot be confused with a confession of blame or guilt as admission is something to admit some facts.