The custom in many communities I have been to is for there to be a siyum on a mesechta on the day of taanit bechorot. All first borns who would otherwise have to fast attend the siyum and are thus exempt from their fast. I would like to know why that is so and why this practice is not utilized for other fast days.
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R. Tzvi Reisman has a long, in-depth discussion on this topic here, and the following are some of the main points which answer the question.
In addition to the standard answer provided by user4523, I heard an explanation that the custom dates to the time of the Temple, when everyone would visit to bring the pesach-offering. The firstborns would observe the Kohamin serve in the Temple, and realize that if not for the sin of the Golden Calf, it would be the firstborns doing the service. Thus the firstborns would feel depressed that they lost their opportunity, and would not eat.
However, the last mishnah in Horayos says that a Torah scholar is greater than a Kohen. By making a siyum, the firstborns comfort themselves by making themselves better than Kohanim. Thus consoled, they are able to eat.
According to this explanation, it is unclear if one can be exempt from the fast due to other types of se'udas mitzvah, such as a circumcision or pidyon haben.