Any country can emit a passport for any person regardless of its citizenship. Case in point, France does not recognize a passport as a proof of citizenship for its own citizen.
The passport is an official diplomatic document stating to other countries that the holder is recognized as written. Having a passport from a certain country entails some prerogatives, like being exempt of visa, or having a passport automatically purported to be valid 6 month after expiration etc....
But holding a passport and having a citizenship are in theory completely different notions, although practically, 99% of the passport are issued by the country of citizenship.