to deny: to say no, refusing a claim, disowning a person, or turning down an obligation.
At its heart this verb means to say no. The one thing it does across every use is refuse: it turns something down, contradicts a claim, or disowns a tie a person is expected to own. The English word deny fits it well, though English deny leans toward calling a statement false, while this word reaches further, all the way to washing your hands of a person.
The three shades below are the same act aimed at different targets. You can deny that something is true, saying it did not happen or is not so. You can deny a person, refusing to be known as their friend, follower, or family, which is the sharp edge Peter felt when he swore he did not know Jesus. And you can refuse an offer or an obligation, turning down a role, renouncing a way of life, or saying no to a demand. Moses refusing to be called the son of Pharaoh's daughter and a believer being told to say no to himself both belong here.
What makes the word carry such weight in the New Testament is not the word itself but what gets denied. To deny that a coin was stolen is a small thing. To deny Christ, to disown the Master who bought you, or to profess God with your mouth while your actions say no, is to break the most basic loyalty there is. The same plain verb covers both, and the seriousness comes from the object, not the vocabulary.