When somebody admits something, they are usually agreeing that something that is generally considered bad or wrong is true or has happened.

admit to agree, often unwillingly, that something is true:It was a stupid thing to do, I admit. · acknowledge (somewhat formal) to accept that something exists, ...

admit of something (formal) to show that something is possible or likely as a solution, an explanation, etc. The situation was too urgent to admit of any delay.

There are 18 meanings listed in OED's entry for the verb admit. See 'Meaning & use' for definitions, usage, and quotation evidence.

admit of something (formal) to show that something is possible or likely as a solution, an explanation, etc.

to agree that something is true, especially unwillingly: He admitted his guilt/mistake. [ + (that) ] She admitted (that) she had made a mistake.

the act of accepting somebody into an institution, organization, etc.; the right to enter a place or to join an institution or organization.

[uncountable] (formal) the right to enter or the act of entering a building, an institution, etc. Hundreds of people were unable to gain admittance to the hall.

admittedly adverb /ədˈmɪtɪdli/ /ədˈmɪtɪdli/ used, especially at the beginning of a sentence, when you are accepting that something is true.

the act of accepting someone into an institution, organization, etc.; the right to enter a place or to join an institution or organization.