Ramazan - the ninth month of the Islamic calendar, occurs in Turkey this year between Wednesday 11th August and Thursday 9th September 2010. Celebrations start at sunset on the previous day - Tuesday 10th August. The dates may vary from country to country depending on whether the moon has been sighted or not.
Ramazan is followed by a 3 day national holiday called Ramazan Bayrami (or Şeker Bayrami) - on 9th, 10th & 11th September. The first day of Seker Bayram is known as Eid al-Fitr, when Muslims will gather to offer a prayer of thanks. You can also expect to see people celebrating at this time.
As şeker means sugar, this particular holiday is marked by a feast of sweet things - it's especially nice for the children. This contrasts with Kurban Bayrami, which will be celebrated at the end of November, where sacrificial animals are slaughtered and the meat is distributed to poorer families.
See the KTLN Kalkan Guide to Şeker Bayram, first published in 2009. Note that the dates change every year, so ignore those for 2009.