Twitter and Turkey have a bit of a love-hate-hate-hate-hate relationship, insofar as Twitter users love to publish unflattering facts about the government, and the government hates that and tries to get Twitter to censor messages. In this particular case, the government is threatening to outright block Twitter unless it takes down "offending" messages.
The current spat is over the Twitter account of left-wing newspaper BirGun, which published details of a police raid on Turkish Intelligence Agency trucks travelling to Syria last January. The trucks were allegedly carrying weapons to support extremists fighting the Assad regime, a fact the government didn't want to become public.
Although Twitter relented to government demands to an extent, removing certain messages from @BirGun_Gazetesi, it didn't block the account entirely. That has angered Turkish officials who, according to the NYT, are threatening a country-wide shutdown of Twitter.
Of course, it wouldn't be the first time that Turkey has shut down Twitter. The last two-week ban in March didn't go particularly well, by some accounts actually increasing traffic during the outage. Maybe someone should teach them about the Streisand Effect. [New York Times]