Calvin is right but we often use "hanging in there" to mean: "I am doing okay (even though the situation is busy / difficult / tough / ...). If we ask it as a question: "(Are you) hanging in there?" Then we are asking how someone is doing in a situation that is busy / difficult / tough / etc.

It means "doing well in a difficult situation". e.g leanrnign Chinese characters well ahahahaha

If you ask how someone is, and they reply "Hanging in there" it means that they are doing fine, or ok.