Dictionary meaning:
Persona non grata
n 1: a diplomat who is unacceptable to the government to which he is sent 2: a person who for some reason is not wanted or welcome
Or this version:
Persona non grata (Latin, plural: personae non gratae), literally meaning "an unwelcome person," is a term used in diplomacy with a specialized and legally defined meaning.
In diplomacy
Under the Vienna Convention on Diplomatic Relations Article 9, a receiving State may "at any time and without having to explain its decision" declare any member of a diplomatic staff persona non grata. A person so declared ("PNG'd" in diplomatic and espionage jargon) is considered unacceptable and is usually recalled to his or her home nation. If not recalled, the receiving State "may refuse to recognize the person concerned as a member of the mission." The opposite of persona non grata is persona grata.
While diplomatic immunity protects mission staff from civil and criminal laws, depending on rank, under Articles 41 and 42 of the Vienna Convention, they are bound to respect national laws and regulations (amongst other issues). Breaches of these articles can lead to persona non grata being used to 'punish' erring staff. It is also used to expel diplomats suspected of espionage ("activities incompatible with their status"), or as a symbolic indicator of displeasure (e.g. the Italian expulsion of the Egyptian First Secretary in 1984). So-called "tit-for-tat" exchanges have occurred, notably during the Cold War and in recent times between the United States and Venezuela.
Non-diplomatic usage
In non-diplomatic usage, calling someone persona non grata is to say that he or she is ostracized, from a person or group, so as to be figuratively nonexistent.