Northern Cyprus was a part of Cyprus that the Turks conquered and annexed. Then, Northern Cyprus declared independence, but it is recognised only by Turkey. Most people think Northern Cyprus isn't really a country and should be ruled from the government that rules the rest of Cyprus. The Turkish army has a large force there which the Turkish Cypriots like while the government of the rest of Cyprus sees them as an occupying force. The United Nations has condemned the occupation.
The United Nations does not recognise Northern Cyprus. If Turkey wants to join the European Union, the EU doesn't want them unless they modify their policy on Cyprus.