In this chapter, the LORD restricts who can eat the holy foods and restates the requirement that sacrificed animals must be without defect.
This chapter is fairly straightforward. We knew that the priests were commanded to eat their share of the sacrifices (the "holy gifts" in this chapter) in a holy place, now we are told that they must eat it while ceremonially clean and that only priests may eat it. Of course, we knew that one must be ceremonially clean to enter the holy place, so this is a natural result of what we were told before.
I don't know the reason why the holy gifts are only allowed for the priest's family to eat. This is just another one of the many restrictions on the holy gifts that make it more clear the priest must have some alternate income to buy or barter for clothing and other stuff, since he's simply disallowed to sell the holy food. Also, there must be some "normal" food for the priests to eat while they are ceremonially unclean. One thing I remember reading about this law is that some priests would try to abuse this command by tricking non-priests into eating the holy food, and thereby earn an extra 20%. Obviously this is not the intent of the command. If I find a reference for this, I will come back and add it here.
The commands regarding sacrifices without defect is very consistent with what I wrote about chapter 21 and is simply an exposition of what the Israelites were already told, that sacrificed animals must be without defect. As is often the case with the Mosaic Law, the author wishes to lay out in specific detail some of the conditions that make an animal "flawed". It is generally consistent with the conditions that disqualify a priest in Lev 21:18-20, with the one peculiar exception that animals with "stunted or overgrown" limbs can be sacrificed as a freewill offering, but not for vows.
We haven't been told the distinction between a freewill offering and a vow, and I don't believe the bible ever makes this clear. My understanding is that with a vow, someone promises to offer a sacrifice if a certain condition occurs (i.e. "If my flock doubles in size this year, I will offer 10 goats to the LORD!"), or something like that. While it is voluntary to make a vow, after that, the person has an obligation to complete whatever they have vowed to do. A freewill offering is an offering that one makes without having any obligation, whether from the law (for instance, the obligatory Passover offering) or from a vow. I can only imagine that freewill offerings are relaxed slightly because they are just that, a voluntary offering. Still, it's hard to explain why only this one exception is made, for this one condition (overgrown or stunted limbs).
In v. 30 we are told a sacrifice of thanksgiving must be eaten on the same day, which is a restatement of Lev 7:15. Freewill and "votive offerings", i.e. offerings related to a vow, may be eaten up to two days after the sacrifice is made and must be burned on the third day. So apparently a sacrifice of thanksgiving falls into a different class than either freewill or vow-related offerings. For whatever reason, we are never exactly told about these different types of offerings; they are only mentioned tangentially in several places. Clearly vows, freewill offerings and thanksgiving offerings were clearly understood tropes to the ancient Hebrew readers, so that there is no need to explain them in the text, but that's unfortunate for us trying to piece things back together. Regardless, I'm pretty sure the thanksgiving offering explains itself: it is an offering made to thank the LORD for some perceived blessing or positive situation.
If in doubt, don't worry about it too much: this is not a particularly important area of the Law compared to the rest.