Two mishnayos earlier, in mishnah 4, we saw that when the paroches became tamei, the place where it is immersed is determined by the level of tumah it contracted. Our mishnah continues this principle, but deals with the meat of kodshei kodashim - meat that must remain in the Azarah and may be eaten only within it.
The rule is that something which became tamei is burned in the place where it is normally eaten, as the principle is expressed: "Kol shenifsal bakodesh, sereifaso bakodesh" - anything disqualified in the Sanctuary is burned in the Sanctuary.
The view of the mishnah:
Meat of kodshei kodashim that became tamei presents four cases, based on two distinctions:
The level of tumah: whether it became tamei through an av hatumah - a severe tumah, or through a v'lad hatumah - a lighter tumah.
The place of the tumah: whether it became tamei inside the Azarah or outside it.
In all of these cases it is burned inside the Azarah, with one exception: if it became tamei through an av hatumah outside. Since this is a severe tumah, we do not bring it into the Azarah in order to burn it there. But if it became tamei through an av hatumah inside the Azarah, even though this is a severe tumah, it is still burned inside the Azarah.
The dissenting view:
According to the dissenting view, in all four cases it is burned outside the Azarah, and only one case is the exception: when it became tamei through a v'lad hatumah - a lighter tumah - and inside the Azarah itself. In that case there is no need to take it out. But if it became tamei through a v'lad hatumah outside, we do not bring it in, even though only a v'lad hatumah is involved.
In summary: our mishnah establishes where the meat of kodshei kodashim that became tamei is burned, based on the principle that whatever is disqualified in the Sanctuary is burned in the Sanctuary. According to the first view it is burned in the Azarah in all cases, except for an av hatumah that occurred outside; according to the dissenting view it is burned outside in all cases, except for a v'lad hatumah that occurred inside.