It is an ancient and widespread custom for the firstborn to fast on the day before Passover. This commemorates the miracle which spared the firstborn Jewish sons from the plague which struck down the firstborn sons of the Egyptians.
By right, this fast should be held on the anniversary of the day on which the miracle occurred: on the night of the fifteenth of Nissan. However, since the fifteenth is already Passover, and we do not fast on Festival days the fast is pushed back to the fourteenth.
There is an additional reason why we fast specifically on the fourteenth. The firstborn of the Jews were saved in Egypt because they humbled themselves before G‑d, admitting and declaring that all greatness, power, and sovereignty are His alone.
This stood in contradistinction to the Egyptians who, filled with foolish pride and egotism, declared: "I am, and besides me there is none other."
Thus, the fast on the fourteenth of Nissan commemorates the fact that the firstborn of Israel humbled themselves on that day and accepted the yoke of G‑d's sovereignty. Abstention from food and drink is a sign of a heart subdued before G‑d.
There are different customs that are associated with this fast. Some maintain that every firstborn, male and female, whether the firstborn is that of the mother or of the father, must fast.
If there are no children, then the oldest member of the household must fast. They base this on the fact that there was no Egyptian household that was spared from the plague, every household in Egypt was struck whether there was a firstborn son or not. We commemorate, therefore, that all of the Jewish households were miraculously spared.
Others maintain that the obligation to fast applies only to firstborn males.
If the fourteenth of Nissan falls on a Shabbat, the fast is observed on the previous Thursday [the twelfth of Nissan], for if a fast is suspended because of Shabbat, it is not held on a Friday. However if the fourteenth of Nissan falls on a Friday, the fast is held on that day. There are some who are lenient, however, and maintain that in this case one does not fast.
There are those who hold that the firstborn sons who are fasting should not fast for the entire day, in order not to enter the Festival suffering, and thus should eat a small amount before the Festival begins.
This fast is treated leniently. Thus, if there is a festive meal held that is connected with a mitzvah, for example, the celebration of a circumcision or of a siyum (the completion of a tractate of the Talmud) the firstborn son participates in the meal rather than fasting.
It is therefore customary to arrange for a siyum to take place in the synagogue after morning prayers on the fourteenth of Nissan. The firstborn sons who are present participate in this festive meal and, having broken their fast, may continue to eat for the rest of the day.