The self-proclaimed Turkish Republic of Northern Cyprus (Kuzey Kıbrıs Türk Cumhuriyeti in the original), often known by the respective acronyms TRNC and KKTC, is the name of the Turkish-occupied northern part of the island of Cyprus.

History

The history of the conflict on Cyprus is a long one, and you can find a decent summary in the node by that name. I'll stick to summarizing the creation of the Republic.

The Coup and the First Peace Operation

After the independence of Cyprus in 1960, Archbishop Makarios was appointed as president. While a moderate respected by both sides, Makarios was Greek and swayed by the strengthening calls for enosis, or union with the motherland, ie. Greece itself -- this being of course anathema to the Turks. Violence erupted in 1963, with a UN peacekeeping force (UNFICYP) sent in to settle things down.

In 1967, a repressive military junta took over Greece, and the Cypriot ardor for enosis cooled -- even the Greeks no longer wanted to unite with a brutal dictatorship. This didn't suit the military though, so they engineered a coup on July 15, 1974 that overthrew Makarios and installed a puppet leader, the convicted EOKA terrorist Nikos Sampson, in his place.

In response, Turkey issued an ultimatum demanding the withdrawal of Greek troops and the reinstatement of the Makarios government, and when it was ignored, it launched the first invasion Peace Operation on July 20, 1974. (To protect the Turkish Cypriots, said Turkey; a convinient excuse, said many others.) The "operation" was successful: the Turks grabbed the northern part of the island, including the vital port Kyrenia, and in two days the military junta in mainland Greece collapsed and Sampson along with it. The exiled Greek president Karamanlis returned, democracy was restored, and the Greek invasion forces were pulled out.

The Second Peace Operation

So all was peaches and cream, right? Nope -- on Cyprus, both sides were still busily engaged in ethnic cleansing, with Turks slaughtering Greeks on the wrong side of the line and vica versa, and they wouldn't stop even when UN Security Council Resolution 353 told them to. The leaders of both sides met in Geneva twice in July and August, but accomplished nothing, while 10000 Turks trapped in besieged Famagusta faced starvation.

So Turkey decided to apply brute force by launching a second Peace Operation(TM) on August 14, 1974. The army advanced until Famagusta on the east coast and Lefke on the west, and then stopped -- and that's where the boundary still lies today, 38% of the island for 18% of the population, with 180,000 Greek Cypriots driven out of their homes into the south.

The Establishment of the TRNC

The stalemate continued, punctuated by a series of fruitless negotiations, until the 1980s, when the UN General Assembly passed a resolution affirming

...the rights of the Republic of Cyprus and its people to full and effective sovereignty and control over the territory of Cyprus and its natural and other sources...
which, to intransigent North Cypriot leader Rauf Denktash, was like being slapped in the face with a raw squid. So, if the UN had decided that those rabble-rousing Greeks on the other side of the border were a legitimate country, the only solution was to match them: and that's why the Turkish Republic of Northern Cyprus declared its independence on November 15, 1983, with Lefkosia (or Lefkoşa in Turkish) as its capital and Denktash as its president. Turkey recognized the nascent republic in April 1984; to date, nobody else has followed suit.

Present

The TRNC is considered as illegal as the Turkish invasion that created it, which means that the would-be republic has been and remains embargoed by the world community: there are no direct links of any sort between the TRNC and the rest of the world, excluding Turkey. Mail, telephone and Internet connections are all routed through Turkey (cf. the TRNC's pseudo-domain nc.tr); there are no flights or ferries to countries other than Turkey either. You can daytrip from southern Nicosia to the northern part, but not vica versa, and a TRNC stamp in your passport will make you a persona non grata in southern Cyprus and mainland Greece as well.

Economically, the north has yet to fully recover from the devastation of the division, and being hobbled by the embargo and the chronically hyperinflating Turkish lira isn't helping at all. Many of the original inhabitants have left and have been replaced by migrants from the mainland. The country remains heavily agricultural, although some tourist industry exists around Kyrenia (Girne) and, due to its agreeable climate and low price level, it has recently found favor with wealthy foreigners looking for retirement homes. The TRNC's GNP per capita hovers around $5000, less than half the south's $13,000, but still considerably wealthier than the nearby Turkish mainland.

Future

Denktash's health is failing and a change in leadership may result in a change of direction. However, now that the South has successfully completed accession negotiations to the European Union, the North has lost its final ace -- there is now very little incentive for the South to negotiate and the stalemate looks set to continue for some time.

References

Personal experience
http://www.pubinfo.gov.nc.tr/
http://www.lonelyplanet.com/destinations/europe/cyprus/history.htm