One of the more popular reddit comments on this. Its been amazing to and watch and read this unfold over the past couple of days.
For those who are asking for an explanation that your average American will understand...
Both by tradition and by constitutional mandate, Turkey is a secular country. Separation of church and state, basically - but just like in the US, there's always been some friction about the degree of separation.
Just like in the US, people in rural areas tend to be more religious, people in urban areas tend to be less so - but keep in mind, when I say "more religious", I am talking about Muslims, but not Jihadis or fundamentalists or whatever term you prefer.
Anyway, the ruling government in Turkey has been increasingly Islamist for the last few years, and has been pushing unusually hard towards the 'more religion' side of the equation. As opposition has increased, the government has become increasingly hostile and repressive.
The Turkish military is a secular organization. Several times in the past when the rural areas of the country elected a ruling group that went too far towards Islamic law in government, the military has stepped in, overthrown the government in a coup, then returned to civil elections once everybody calmed down.
So is Turkey headed for a Syrian-type civil war? No. The Turkish police are under the thumb of the government, but the military is not, and just like in Egypt, the military is the real power. If the current government is overthrown, there will be elections again - but unlike Egypt, fundamentalist organizations don't have major power in Turkey, and are unlikely to wield a controlling influence.
EDIT: Spelling.
EDIT 2: Let me clarify one thing that seems to be causing a lot of confusion. When you say 'government' to an American, they tend to think of the entire permanent edifice of governing - everything from the congress to the IRS to the EPA to the military. But Turkey has a parliamentary system (like the UK) so when you say 'government' in that context, you're talking about the ruling (or majority) party.
Like for example, when "Nigel Snuffleknickers has been elected Prime Minister, and will now begin assembling the new government" - it doesn't mean the whole thing gets scrapped and rebuilt. It just means new people in charge.
From what I'm getting the occupy part of this really picked up steam because of the local media blackout, and people have started in mass to pull their money out of the banks that are connected to said media.