To misread something is to read it but understand it in the wrong way. If you misread an article about local politics, you might end up supporting a candidate whose views you don't actually agree with.
When you interpret a book, online article, or magazine story incorrectly, you misread it. You can also misread people, when you don't understand how they feel or what they intend: "She tended to misread cranky customers at the coffee shop, thinking they were joking when they were actually angry about something." The prefix mis- means "bad" or "wrong," and read can mean both "comprehend printed matter" or "make out a person's character."