When someone's narrow-minded, they're intolerant of other people's opinions and experiences. There's no convincing your narrow-minded uncle that Indian cuisine is delicious — he stubbornly insists that only "American" food tastes good.
Being narrow-minded means that you've got a rigid and ungenerous perspective on the world. It's narrow-minded to believe that everyone who disagrees with you is wrong. A narrow-minded person can see only their own tiny slice of the world and doesn't attempt to learn about and understand other people's experiences. Prejudiced and biased people are also narrow-minded: "The narrow-minded opponents of integrated schools were on the wrong side of history."