Hello Julia, "I don't mind" means " I don't take any offense at something" Usually it is something unpleasant or disgusting as to the senses,nevertheless it doesn't really offend you. It could be something causing disturbance or annoyance. Example: "Do you mind if I smoke?" "No, I don't mind at all." **In the example of "I don't mind coffee" here it said to politely accept an offer of food or drink. It indicates having no preference. Another similar example: "There's plenty more cake if you'd like another piece." "I don't mind if I do." ** In another context it is a gentle statement allowing something to happen or approving it. " Do you mind if I use your phone?". " I don't mind at all." However the meaning could be slightly different in various contexts. Where it means in some contexts "It doesn't bother me , I give you permission",it could in others show one is indifferent or encouraging.

It means that it doesn't worry me or that you are neutral about person xxxx, you neither like nor dislike xxxx

I don't mind answering your follow-up question. :) "I don't mind him" - > I ignore him. Usually used with Imperatives: "Please, don't mind the mess" -> Please, don't pay any attention to the mess. "Eh, don't him: he just quietly sits there all day." -> Please, just ignore him; don't be bothered by his presence.