The Fast of the Firstborn (Ta’anit B’chorot) commemorates the horrific tenth plague that God inflicted on Pharaoh and the Egyptian people. After Pharaoh had again refused to let the Children of Israel go, Moses warned of the impending plague that would see the death of every first-born son in the land.
The sons of the Israelites were spared because their families sacrificed a lamb and put some of its blood on the doorposts of their homes, allowing the Angel of Death to ‘pass over’ the Jewish homes. This is where the English name ‘Passover’ for the festival of Pesach comes from.
In thanksgiving for their survival, the first-born son in a Jewish family fasts from dawn on Erev Pesach (the day before Pesach) until the Pesach Seder. The mitzvah to fast on this day is d’Rabbanan (from the rabbis) rather than from the (written) Torah. As with other ‘minor’ fast days, the fast is observed by fasting (abstaining from all food and drink) from sunrise until nightfall. If a simcha (happy occasion) such as a betrothal or the completion of study of a tractate of Talmud falls on Erev Pesach, a person may eat in order to celebrate performance of the mitzvah. In order to exempt first-born sons from the rigours of fasting, most synagogues arrange that someone completes the study of a tractate of the Talmud at morning prayers; everyone present then joins in a small celebratory meal to mark the occasion. This then exempts the first-born sons from fasting for the rest of the day since the rule is that a fast, once broken on a particular day, is not resumed.
Chabad.org: The Fast of the First Born
Akhlah: Ta’anit Bechorot
My Jewish Learning: The Fast of the First Born