Most people really don't know what to expect when you say you're eating Cypriot Food. Most people assume that Cyprus is a Greek island (which is wrong) so they just assume that the food will be exactly the same as what you would find on other Greek islands. While there is a great deal of Greek influence on Cypriot cooking, there is also some influence from other parts of the Mediterranean, as well as a little British flavour. You also can't forget that across the Buffer Zone is an area occupied by Turkey, thus there are some great Middle Eastern foods availble in parts of the island as well.
Restaurant wise you are going to find many Greek Cypriot style tavernas, particularly in tourist areas. These tavernas do have a Greek feeling about them, but they offer a few unique dishes that are truly Cypriot in nature. The most famous Cypriot dish is Haloumi cheese. This is a salty cheese that is grilled, sometimes fried, and never melts. Cyprus is also very famous for their sweet treats, including walnut spoon sweets and Lokum.
One of the other great things about eating in Cyprus is that they have a much broader choice of foods when compared to the Greek islands. You're more likely to find a good British Pub, or fine Indian restaurant in Cyprus than you are in most of the Greek islands. All that and by simply crossing the border you have a huge range of Turkish food available as well.