To misinterpret means to understand something incorrectly or in a way different from what was intended. When you misinterpret a friend's joke as an insult, you've gotten the wrong meaning from what they said. When a student misinterprets the instructions on a worksheet and solves the wrong problems, they've misunderstood what the teacher wanted them to do.

A misinterpretation is the incorrect understanding itself: “His frown was a misinterpretation of her silence; she wasn't angry, just thinking hard about the problem.”

Misinterpreting happens all the time because communication is tricky. Someone might misinterpret your facial expression, thinking you're bored when you're actually concentrating. You might misinterpret a poem in English class, missing the symbolism the author intended. Text messages are especially easy to misinterpret since you can't hear someone's tone of voice or see their expression.

The key difference between misinterpreting and simply not understanding is that when you misinterpret, you think you understand, but you've gotten it wrong. It's not that the meaning is missing; it's that you've landed on the wrong meaning entirely.