Ta'anith Esther (the Fast of Esther) is held on the 13th of Adar, the day before Purim. The Shulhan 'Aruch states that when this falls on Shabbath, the fast is brought forward to the preceding Thursday. This is because we may not fast on Shabbath, and we prefer not to fast on a Friday so as not to enter Shabbath while in an unpleasant state.
The Rama adds that if there is a Milah on that Thursday, the participants are permitted to eat at the Se'uddah (festive meal), but those who ate must fast on the following day (Friday). Some Aharonim state, however, that if there is a Milah on Thursday, the Se'uddah should be held at night as is done on other fast days. There are those who say that the parents of the child together with the Sandaq and Mohel are permitted to eat and do not need to fast on Friday.
If someone was traveling on that Thursday and forgot about the fast, but when he returned home at night realized his error, he should fast on Friday.
(See Sh. A. 686: 2 with Rama. Kaf Hahayim ibid, 24, 27, 28. M.B. ibid, 7)
