The police are retreating from the main protest area (Taksim square in Istanbul) now, this is huge.
Historical background here is that Turkey's cities & west tend to be more secularist, the countryside and south/east more religious. Istanbul is particularly secularist; the idea of Turkey according to its founder, Kemal Ataturk, was to be a fully secular state, and this is upheld by the judiciary and military mostly. The democratic government are more Islamist now though and a lot of secular Turks are worried about a greater public role for religion. Apparently there are protests in Ankara as well as Istanbul (Ankara is the actual capital, Istanbul is the largest city but not the capital).