Someone who's mistaken is confused or wrong about something. If you think your guidance counselor is mistaken about what you should do with your life, you will probably ignore his advice.
If you see a car speeding through town, you might assume the driver is a teenager — but you'd be mistaken if the car is actually driven by an elderly lady. You also might believe someone else is mistaken if their opinion seems wrong to you: "You think strawberry ice cream is better than chocolate, but you're mistaken." Mistaken comes from mistake, from its Old Norse root mistaka, "take in error."