It's worth doing a little bit of reading about the history of the Papal States.
http://en.wikipedia.org/wiki/Lateran_TreatyThe Lateran Treaty is one of the Lateran Pacts of 1929 or Lateran Accords, three agreements made in 1929 between the Kingdom of Italy and the Holy See, ratified June 7, 1929, ending the "Roman Question".
They consisted of three documents:
- A political treaty recognizing the full sovereignty of the Holy See in the State of Vatican City, which was thereby established.
- A concordat regulating the position of the Catholic Church and the Catholic religion in the Italian state.
- A financial convention agreed on as a definitive settlement of the claims of the Holy See following the losses of its territories and property.
As to why it still is a state. One explanation: The political reality of The Vatican as a sovereign state was established under formal and binding treaty. Its sovereignty is recognised by most countries. It has as much right to exist as any other country on the planet. IE No state or nation has a moral right to exist;there is no 'should', only 'is 'or is not'.