To not worry about or care about something; "don't worry/about it."
気にしないで、誰にでも間違いはあるよ。
Don't worry — everyone makes mistakes.
遅刻しても彼はあまり気にしないタイプだ。
He's the type who doesn't worry much even if he's late.
その件については私はもう気にしないことにした。
I've decided not to worry about that matter anymore.
天気が悪くても気にしないで出かけよう。
Let's go out without worrying about the bad weather.