Before us are the Shelamim (peace offerings), which constitute the primary model of kodashim kalim (offerings of lesser sanctity). The Mishnah separated them from the two offerings listed in the previous Mishnah because their timeframe is longer: two days and the night between them. This is the most common type of offering, after the Olah (burnt offering).
Two ways in which the Shelamim are brought:
Voluntary Shelamim: A person who wished to bring an offering to God and eat of its meat - a common occurrence during the time of the Temple - would bring a voluntary Shelamim. The offering was sacrificed, and afterward, they ate from it.
Obligatory Shelamim: There is an entire category of Shelamim brought out of obligation - the Shalmei Chagigah (festival offerings). Three times a year, when going up to the Temple on the three pilgrimage festivals (Pesach, Shavuos, and Sukkos), a person is commanded not to appear empty-handed before God, but rather to come with two types of offerings: an Olas Re'iyah (appearance burnt offering), followed by Shalmei Chagigah - Shelamim brought out of obligation.
In addition, on every day of the festival - including the days of Pesach, Sukkos, and Shemini Atzeres - there is an obligation to rejoice, which requires eating sacrificial meat every single day. One who has another offering to bring, such as the tithe offering, may bring it and eat from it; but if there is no other sacrificial meat around, one of the family members or friends must bring Shalmei Simchah (offerings of rejoicing) - additional Shelamim for the purpose of rejoicing, which are also brought as voluntary offerings - and eat their meat on every day of the festival.
The language of the Mishnah:
"Hashelamim kodashim kalim" - their status, as explained above, is kodashim kalim, and therefore their slaughter may take place anywhere in the Courtyard. Their blood requires two applications that are four - on the northeast and southwest corners, according to the law of the previous offerings.
The meat, both the portion of the one bringing the offering and the priestly gifts that will be discussed below, is eaten anywhere in the city of Jerusalem, by any person - without restrictions such as requiring one to be a kohen and the like - and through any method of preparation and eating, unlike the Pesach offering.
The time for eating:
The timeframe is broader than anything we have seen so far: two days and one night. It is possible to eat from the meat on the first day, as well as on the second day - even though its taste is already diminished, as it has begun to spoil. Not only that: one who did not eat the meat on the first day while it was still fresh, as is proper to do, must eat it on the second day, because otherwise the meat will remain past its time - and the prohibition of nosar (leftover sacrificial meat) is a Torah prohibition.
The separated portion - the priestly parts:
"Hamuram meihem kayotzei vahen" - the parts separated and given to the kohanim are the breast and the thigh, as we saw with the Todah (thanksgiving offering): the breast is the portion from the animal's chest, and the thigh is the right hind leg. Their law is the same as the law of the rest of the meat: they are eaten within Jerusalem, for two days and the night between them.
"Ela shehamuram meihem ne'echal lakohanim" - their law differs on one point: the breast and the thigh are eaten by the kohanim alone - by them, their wives, their children, and their slaves. As was explained in the previous Mishnah: "their wives" - those actually married to them; "their children" - the children living in their home or who are part of the family, and not daughters who married non-kohanim; "their slaves" - Canaanite slaves, meaning non-Jewish slaves, and not Hebrew slaves.