This is a phrase that's most often used by parents or teachers talking to misbehaving children. You say "Don't make me (do something)!" to threaten some kind of punishment. For example:
Don't make me come up there!
Don't make me call your mother!
As you can see, the parent doesn't directly state what the punishment is going to be; it's just a vague threat of something bad that's going to happen if the child continues to behave badly.