It would generally mean "to stop bothering me" about something. Example: John: Sally, you need to study for your test. Sally: You've told me this many times. Get off my back about it. From this example, John is telling Sally to study more, which he has done many times. Sally is getting tired of hearing John tell her this frequently. So she tells him to stop mentioning it by saying to "get off my back." So, while in some sense it does mean "leave me alone," it is only for a specific thing. The person wouldn't necessarily want to left alone. They just wouldn't want to talk about certain things.

The expression, "get off my back" is used when you want another person to stop pressuring you. For example, if your friend repeatedly asked if you could help them with a homework assignment, you might say, "Get off my back. I told you I can't! You have to do it yourself".