To avoid making a judgment or decision about things before thoroughly considering them. If you're not going to have an open mind about this, I don't see how we're going to have a productive discussion about it. I know you think that Morton is a dullard, but try to have an open mind—once you get to know him better, you'll find that he's really quite funny.

To avoid making a judgment or decision about someone or something without full knowledge about them or it. I know you think that Morton is a dullard, but try to keep an open mind—once you get to know him better, you'll find that he's really quite funny. I don't usually like musicals, but I'm keeping an open mind.