The Treaty makes us all real citizens of this new European Union for the first time, instead of our being notional or honorary European "citizens" as at present:-

A State must have citizens and one can only be a citizen of a State. 

Citizenship of the European Union at present is stated to "complement" national citizenship, the latter being clearly primary, not least because the present EU is not a State. It is not even a corporate entity that can have individuals as members, not to mind citizens. By transforming the legal character of the Union, the Lisbon Treaty transforms the meaning of Union citizenship. Article.17b.1 TEC/TFU replace the word "complement" in the sentence "Citizenship of the Union shall complement national citizenship", so that the new sentence reads: "Citizenship of the Union shall be in addition to national citizenship."  

This gives the 500 million inhabitants of the present EU Member States a real separate citizenship from citizenship of their national States for the first time. It gives a treble citizenship to citizens of Bavaria and Brandenburg within a Federal State like Germany. The rights and duties attaching to this citizenship of the new Union are be superior to those attaching to citizenship of one's own national State in any case of conflict between the two, because of the superiority of EU law over national law and constitutions.  As most States only recognise that one can have a single citizenship, henceforth it is one's Union citizenship which will be regarded by other countries as primary and superior to one's national citizenship. 

Although we will be given rights as EU citizens, we should not forget that as real citizens of the new European Union we also owe it the normal citizens' duty of obedience to its laws and loyalty to its authority, which will be a higher authority than that of our national States and constitutions.  Member States retain their national constitutions, but they are subordinate to the new Union Constitution.  

As such they will no longer be constitutions of sovereign States, just as the various local states of the USA retain their constitutions although they are subordinate to the Federal US Constitution.