In this chapter, the LORD gives Moses the regulations of the sin offering.
Beginning right in verse 2 we can see that this is a sacrifice of atonement for accidental sin with regards to "things which the LORD has commanded not to be done," i.e. the prohibitions of the Law of Moses. I'd like to point out that there is no atonement for intentional sin, possibly because intentional sin is punishable by death and there is no atonement for it. But possibly this is because the text here is making a presumption that people will not willfully violate the covenant. Certainly we see this presumption later in verse 14, because if the whole congregation sins intentionally, then what could that mean but the destruction of the whole nation? We had already seen their potential destruction in Ex 32, with the result that Moses prayed for mercy to avert disaster. Even then, some thousands of the people still died.
Anyway, there are four different types of offerings listed here depending on who commits the unintentional sin: in order, there is the high priest, the general community, "a leader", and "anyone of the common people". In general terms, these four different sacrifices are nearly the same. The main difference is that the high priest and the community are expected to sacrifice bulls, which are more expensive than the goat offering of a leader and the goat or lamb offering of the people. This is because the high priest and the whole community are expected to have more wealth available than the other two groups, so it is reasonable that they could sacrifice more lavishly.
Another interesting difference amongst the four offering types is that in the first two, the flesh of the bull must be burned outside the camp, but for the last two, it is not specified what is to be done with their flesh. Possibly it is given to the priest, I guess we'll find out in a few chapters. Sin offerings are expected to be more rare (you can only unintentionally sin until you find out: after that, it's intentional), so maybe it's considered less important what happens to the animal.
As I noted above, with regards to the sin offering of the high priest and the community, the fat is burned on the altar and the flesh and hide are burned outside the camp. As with the burnt offering and peace offering, the offerer (either the high priest or the "elders of the congregation") is to lay his hand on the bull's head, to transfer his sin and guilt to the animal, and this is possibly related to why the animal is burned outside the camp. The idea of burning it outside the camp is to physically bring the sin away from the people, after transferring it from the sinner to the animal. Back in Exodus 19:13, we are told that any man or animal who touches the mountain is to the stoned or shot with arrows, and is not to be touched. As with here, that shows a presumption that physical contact with a sinner transfers the sin. In Ex 19, touching a sinner brings that sin into the person who is touching the sinner, and here, touching the animal brings the sin into the animal.
Therefore removing the animal from the camp also removes the sin to a place where it cannot "infect" any of the people who are within the camp. I don't know why this is the case for the sin offering and not the earlier substitutionary offerings (burnt, peace). Possibly it's because this offering is more directly focused on the removal of sin, while the earlier offerings it was more tangential to their purpose.
In the case of all four sacrifices, the high priest is supposed to do something or other with the blood (sprinkle some, paint some on the horns of the altar of incense, pour the rest out on the ground, basically just get blood everywhere). As with the peace offering, the fat is always burned on the altar: in fact, this chapter refers to doing things "just as the... peace offerings" (v. 31). Unexpectedly, the gender of the first three sacrifices (high priest, community, leader) must be male, while the gender of the last sacrifice (common people) must be female. It's peculiar to me that the commoners must sacrifice females, given that females are more expensive, but also because I would have expected these various classes of sacrifices to be more consistent. At the end of the day, I am not aware of any particular significance to this difference, so there isn't much more that I can say about it.