In this chapter, the LORD instructs Moses on the regulations of the peace offering (also known as a fellowship offering).
The first thing to note about this chapter is that it is largely similar to the burnt offering of chapter 1. There are some differences however.
The peace offering allows the sacrifice of a male or female, while the burnt offering only allowed the sacrifice of a male. I don't know why they made this distinction. When it comes to animal genders, note that the females are typically more valuable than the males. This is interesting because as it regards to people, the culture of that time valued male children more than female, because it was the male child that carried on the family line. When it comes to animals however, more practical concerns dominate: to wit, it only takes a single male to impregnate many females, while each female can only bear a single child at a time. So in order to grow one's herd very rapidly, only a handful of males are required, while every single female can contribute by bearing forth offspring every year. That means you can sacrifice male offspring with few consequences to the general growth rate of your herd, and hence their value.
Offering males, then, would be the cheaper of the two genders to sacrifice, even though when it comes to human society the people would think the opposite.
In the ritual of the peace offering, the only part that is supposed to be burned in the fire is the fat of the sacrifice. All of the meat is retained and contrary to the earlier sacrifices, it meant to be eaten by the offerer and not the priest. This is because the sacrifice is meant to be a shared meal between the offerer and the LORD, with the fat (i.e. the best part with the most calories) burned and given to God (in a sense), and the rest eaten by the worshiper. I have previously emphasized the importance of sharing meals in the bible, as it pertains to ratifying covenants. We could think of this meal as being similar. In addition, this shared meal allows for a sense of identification or friendship between the LORD and the offerer: hence the name, peace offering or fellowship offering.
The last big difference I see is there is no statute for the sacrificial offering of birds in the peace offering, while that is allowed for burnt offerings. I would guess the reason is that the peace offering is rarely (if ever) required by statute for the people to maintain ceremonial cleanliness or to obey the law of the covenant. That is, this sacrifice is largely voluntary, and so there is less reason to consider the financial status of the person trying to make the offering, because logically if there is a poor person who cannot afford it, they are under no obligation to do so. Contrariwise, the burnt offering is required under a variety of conditions in order to maintain compliance with the law, so it is necessary to make it possible for all of the people to make a burnt offering on occasion.
After mentioning all of these differences, there are also many similarities. We see the placing of one's "hand on the head of" the offering, a self-identification with the sacrifice and a transference of guilt to the animal (i.e. substitution). It's interesting that even a peace offering involves the transference of guilt. It seems like every sacrifice involves some acknowledgement of the sinfulness of the offerer and a corresponding purge of that sin.
We also see that the priest again sprinkles blood around the altar, because as with the Passover, it is through the shedding of blood that the people are protected from the Genesis 3 death. There are a few more minor details, but that's pretty much it for the peace offering.