A misinterpretation is when you understood something, but understood it wrongly. Notice that this is different from not understanding at all — with a misinterpretation, a meaning did arrive in your head; it was just the wrong one. You read the message, you heard the speech, you looked at the numbers, and you walked away sure of something that was not what the other person meant, or not what the facts actually showed. So it is the confident kind of mistake, which is why it can cause so much trouble before anyone notices it.

You use it about words, but also about actions and about evidence. Someone smiles at you in a meeting and you decide they agree with you — that is a misinterpretation of their smile. A scientist looks at the same data as another scientist and draws the wrong conclusion — a misinterpretation of the data. Lawyers and translators use the word a lot, because their whole job is meaning, and a wrong meaning is a serious problem.

The word is a little formal. In everyday talk people say "you got me wrong" or "that's not what I meant". You meet misinterpretation more in writing: news reports, work emails, school essays, notes on a contract. It often comes with words like open to, lead to, avoid, clear up: "The sentence is open to misinterpretation" means the sentence is written in a way that invites people to take it wrongly — a warning about the sentence, not about any particular reader.

One more thing, though. English has a polite habit here. People often say "I think there's been a misinterpretation" when what they really mean is "you were wrong" — the noun lets you point at the mistake without pointing at the person. That softness is part of how the word is really used.