Boureki can be anything sweet or savoury in a pastry-- many things that a Greek would call a pita. One everyday day in Greece where the word has survived is galaktoboureko. In Chania, Crete, they make χανιωτικο μπουρεκι (Chaniotiko boureki) baked with slices of potato, zucchini (courgette), myzithra and mint. On Chios they make bourekia stuffed with pumpkin, fennel, feta and grated myzithra.
The word comes from the Turkish börek, and to this day all the countries that were once part of the Ottoman Empire make their own versions--including Israel, where many Sephardic Jewish families who once lived in the Ottoman Empire, (specially in Thessaloniki), took refuge during the cataclysms of the 20th century. The Cypriot word is the similar poureki (πουρέκι).
Image by Eelke