It's an idiom (meaning it's an expression that can be hard to explain). You can ask someone if they mind if you sit next to them, or "do you mind" if I read off your menu? That means you don't want to be a nuisance, but if they don't care, you would like to do something. The person may be a nice person, and they will say, "no, go ahead, I don't mind. That won't bother me".

You can use it to demonstrate you are not interested or concerned in something.

I don't care

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I don't mind= it does not worry me/ it's ok with me