We learned in the Mishna (19a) that Beit Shammai restricted the kinds of sacrifices that could be brought on Yom Tov to those that are obligatory on those days, while Beit Hillel permit all types of sacrifices to be brought.
Hillel and Shammai lived at the end of the Second Temple period, so their disagreement is not one that involves only theoretical principles, but practical ones, as well.
The Sages taught in a: There was an incident involving Hillel the Elder, who brought his burnt-offering to the Temple courtyard in order to place his hands on the animal’s head on a Festival. The students of Shammai the Elder gathered around him and said to him: What is the nature of this animal that you are bringing? Hillel, being humble and meek, did not want to quarrel with them in the Temple and therefore concealed the truth from them for the sake of peace. He said to them: It is a female, and I have brought it as a peace-offering, as burnt-offerings are always male. He swung its tail for them so that they would not be able to properly discern whether the animal was male or female, and they departed.
A korban olah (burnt-offering) is totally burned on the altar, and none of it is eaten – neither by the kohanim nor by the person who brings it. A korban shelamim (peace-offering) is a sacrifice where part is offered on the altar, but there are also parts that are eaten by the kohanim and by the owner. According to Shammai, a korban olah cannot be brought on Yom Tov. A korban shelamim, however, can be brought, since parts of it will be eaten by the kohanim and by the owner, making it not only a sacrifice, but also food preparation, which is permitted on Yom Tov. Beit Hillel permit both olot and shelamim to be brought since they are connected to the holiday. Hillel’s conciliatory stand taken in our led to a situation where the students of Shammai were ready to claim victory and have the final ruling on this matter follow Shammai’s teaching.
At that moment, Bava ben Buta, one of Shammai’s students who recognized that Hillel’s position was the accepted one, stepped forward and arranged for a large number of choice cattle to be brought to the Temple. He called upon the onlookers to perform semikha on the animals and bring them as sacrifices, which was a public admission that Hillel’s position was to be accepted. From that time on there was no longer any debate on this matter.
The Talmud Yerushalmi relates the story in a slightly different manner, reporting that Hillel’s modesty almost led to the acceptance of Shammai’s position. At that moment the Temple emptied of korbanot, since no one was willing to come to sacrifice. This led Bava ben Buta to curse the people who brought on this situation, saying “the houses of these people should be made desolate, just as they made desolate the house of our Lord.” He then ordered 3,000 cattle brought and announced that people should resume bringing sacrifices, so that the mikdash should not stand empty on Yom Tov.