When you don't want to listen to someone's conversation, or hear what they have to say. When you could care much much less about what they have to say.
Person A: PENGUIN LOVE ! :D
Person B: I don't care what you have to say. It is random and unnecessary.
don't care means that you do care but you just don't want to tell them that you do
girl:hey do u think i should ask jake out?
boy who likes girl:i don't care...