In less than four minutes, this video pretty much sums up what the Turkish people are currently protesting.
It started off as a demonstration against turning Taksim Square and one of the few small sections of green in Istanbul- Gezi Park- into a 19th century Ottoman barracks which would house a shopping mall, possibly a museum and luxury apartments, but has escalated into something far bigger: anti-government protests. Dissatisfaction with the conservative ruling leadership which, under Prime Minister Recep Tayyip Erdoğan, has been attempting to turn secular Turkey into more of an Islamic state. The secular in that country are not happy about this.
The video outlines some of their gripes.
It doesn't help matters that protesters have been met with violence.