Maseches Beitzah, chapter two, mishnah 4. Before we look at the words of the mishnah, some background: there are several types of offerings that a person is obligated to bring on Yom Tov.
The offerings that must be brought on Yom Tov:
Shalmei chagigah - a peace offering from which the owners who bring it eat, while certain portions are eaten by the kohanim and others are burned on the altar. A person is obligated to bring it on Yom Tov.
Shalmei simchah - an offering brought in a case where a person has no other meat to eat.
Olas re'iyah - a burnt offering that is consumed entirely on the altar. Its purpose is appearing before Hashem: a person comes and brings an offering to Hashem.
The view of Beis Shammai:
"Beis Shammai omrim: mevi'in shelamim" - one may bring the shalmei chagigah or the shalmei simchah on Yom Tov, because they are brought for the purpose of eating, and work needed for preparing food is permitted on Yom Tov.
However, every private offering requires semichah beforehand: the owner of the offering places his hands on the head of the animal and presses down with all his strength. According to Beis Shammai, semichah involves leaning the weight of one's body on the animal - if the animal were to be pulled away, the person would fall - and it is forbidden to make use of a living creature and exploit an animal on Shabbos and Yom Tov.
"Ve'ein somchin aleihem" - therefore one may not perform semichah on Yom Tov; rather, the semichah must be done in advance, on erev Yom Tov. Beis Shammai does not hold that the semichah must come immediately before the slaughtering.
"Af lo olos" - likewise, one may not bring a burnt offering on Yom Tov, since it contains no element of food preparation and is offered entirely to Hashem. Even the olas re'iyah must be brought after the first day of Yom Tov, during Chol HaMoed; and on Shavuos, during the days of tashlumin that follow it.
The view of Beis Hillel:
"U'Beis Hillel omrim: mevi'in shelamim ve'olos" - one may bring the shalmei chagigah and the shalmei simchah on Yom Tov, as Beis Shammai holds, and the olas re'iyah as well.
"Vesomchin aleihem" - the semichah is permitted too, because according to Beis Hillel the semichah must be performed immediately before the slaughtering, and it cannot be moved up to erev Yom Tov. Therefore, even though there is a rabbinic prohibition against making use of animals, it was permitted here because of the halachic requirement of semichah.
Vow offerings and free-will offerings:
Even Beis Hillel agrees that offerings brought as vows or as free-will gifts, which are nothing more than a gift, may not be brought on Yom Tov - neither burnt offerings nor peace offerings - and must be brought on another day during Chol HaMoed. And even though peace offerings are eaten, since bringing them is not mandated by the Torah they are not brought on Yom Tov, for one who eats from an offering eats from the table of the Most High, from the table of the Holy One, blessed is He: the offering is brought to Hashem, and the person eats from it as a byproduct, but its essence is an offering to Hashem and not personal food preparation.
In summary: in this mishnah Beis Shammai and Beis Hillel disagree about bringing offerings on Yom Tov. According to Beis Shammai one brings only peace offerings, because they involve food preparation, one does not perform semichah on them on Yom Tov but rather on erev Yom Tov, and one does not bring burnt offerings. According to Beis Hillel one brings burnt offerings as well and performs semichah on them, since the semichah must come immediately before the slaughtering. And according to all opinions, offerings brought as vows or free-will gifts are not offered on Yom Tov.