How is it so hard to define? It means people should be allowed to do as they like without the government snooping and interfering, as long as they're not harming another person unlawfully. The debate regarding abortion then is over whether a fetus is a person, not over whether people have a right to privacy.
No, it doesn't mean that. It means being apart from company or observation. Wiki defines it as "the ability of an individual or group to keep their lives and personal affairs out of public view, or to control the flow of information about themselves" which seems a pretty good definition and shows why government how government can go too far in protecting it.
How about if the government suspects one is harming another? Can it snoop? How about if you run a red light at 2 a.m.? Can it interfer?