What is Admit?

Legal Definition
1) To state that a certain fact is true. 2) In a civil case, to state that a plaintiff's allegation is true. If a defendant admits an allegation, the plaintiff need not prove it at trial. 3) In a criminal case, to state that a certain fact is true or to acknowledge guilt. 4) At trial, to allow, inter alia, testamentary or documentary evidence to come in for a judge or jury to consider in reaching a decision.
Illustrative caselaw
See, e.g. Ohler v. U.S., 529 U.S. 753 (2000) (admitting evidence) and Burley v. German-American Bank, 111 U.S. 216 (1884) (admitting an allegation).
See also
Legal Definition
To allow, receive or take; to suffer one to enter; to give possession; to license. Gregory v. United States, 17 Blatchf. 325, 10 Fed. Can. 1195. See Admission.
-- Black's Law Dictionary