Moses destroyed the Golden Calf, and re-ascended Mount Sinai to plead G-d's forgiveness for the Jewish people. (Exodus 32:20; Talmud Taanit 30b. See "Today in Jewish History" for Tammuz 16 and Tammuz 17)
Because of the holiness of Shabbat, the fast of Tammuz 17 is this year postponed to today, Tammuz 18. We refrain from all food and drink from "daybreak" (about an hour before sunrise, depending on location) until nightfall. Special prayers and Torah readings are added to the day's services.
The fast day mourns the breaching of Jerusalem's walls and the other tragic events that occurred on Tammuz 17--see "Today in Jewish History" for that date--and repenting and rectifying their causes.