also: いえ
Polite negative answer to a yes/no question or statement. In casual speech, ううん or いや are more common.
「コーヒーはいかがですか?」「いいえ、結構です。」
"Would you like some coffee?" "No, thank you."
you're welcome; not at all; don't mention it
Used to modestly deflect thanks, similar to 'it was nothing'. Often repeated: いいえ、いいえ.
「手伝ってくれてありがとう。」「いいえ、どういたしまして。」
"Thank you for helping me." "You're welcome; it was no trouble at all."
No, I am not a student.
Not at all, thank you too.
否 is a formal, literary noun for 'no' used in writing and formal decisions, while いいえ is the everyday spoken word for 'no' in ordinary conversation.