I've been following the events since the beginning (in fact I was there at the solitary meeting in Chicago yesterday:
http://www.chicagotribune.com/news/local/breaking/chi-local-...), so let me summarize what's been going on. However, if you have time to read just a single post, read this (
http://technosociology.org/?p=1255) spot on analysis instead of my comment.
First, it's not an Istanbul thing anymore, many Turkish cities, especially Izmir and Ankara witnessed large protests and clashes with the police in the past couple of days.
On paper, this started with a small group of protesters sitting in the park to stop its demolition and cutting down the trees on Monday. That evening and at 5am on Tuesday morning they were violently attacked by the police. The attacks continued on Wednesday. The appalling police brutality unfortunately is nothing new in Turkey but this time it triggered an unexpected reaction from a wide swath of people.
People's discontent with AKP has been rising for some time, although they have provided a stable economy for the past 10 years. Some of the recent events have really notched it up, though, e.g.:
* The fact that government made no official plans to celebrate the May 19th holiday, which is an important day in the creation of the Turkish Republic (mirroring their approach to the October 29th holiday, which is like July 4th for Turkey)
* Lack of adequate response from PM Erdogan to the bombing in Reyhanli. Rather than cancel his visit to the US to visit the town, he went with his original plan. A lot of people thought that he brought such terrorist activities on Turkey due to his agressive rhetoric on Essad and his strong support of the dissidents there.
* The recent ban on the sale of alcohol between 10pm and 6am (http://www.guardian.co.uk/world/2013/may/31/turkey-alcohol-l...). This was an unheard-of move that angered a lot of people, not because Turkey consumes a lot of alcohol but it was interpreted as a step to the Islamic Law.
What really surprised me (and I witnessed many a protest and a few military coups there) was the exponential growth of the protest and its apolitical nature. Before, people used to write the usual leftist slogans on the walls, this time there were a lot of funny graffiti about Erdogan, the police and the pepper gas (examples at https://eksisozluk.com/gezi-parki-isgali-duvar-yazilari--385..., for Turkish readers).
Due to the wide use of social media there were some disinfomation as expected, spread around by excited people, e.g. that the police was using Agent Orange. This was due to the China-like complacency of the Turkish media. In fact, when CNN International was transmitting live from the riots in Istanbul CNN Turk was running a documentary about penguins! The reason for this is two-fold: the intimidation of reporters in the past 2-3 years (e.g. see the OdaTV case, where the owner of a TV station and reporters were swiftly jailed with scant evidence when they criticized the government: http://www.nytimes.com/2012/12/28/world/europe/soner-yalcin-...). The other reason is the financial blackmail that the government exercises over large media conglomerates, e.g. when the Dogan group got a colossal $2.3B tax fine in 2009.