This mishnah continues the discussion of the previous one. The previous mishnah dealt with the question of sacrificial meat that became tamei - where it is burned. The distinction there was based on a case in which two conditions were combined: that the meat was tamei and that it also left its designated place - that is the only case in which it is burned outside, and in all other cases it is burned inside. And the same in reverse: only in a case where the meat was tahor and its disqualification occurred inside is one permitted to burn it there.
The view of Rabbi Eliezer:
In our mishnah, "Rabbi Eliezer omer" - Rabbi Eliezer says, and he rules that everything depends on whether the meat contracted the severe tumah of an av hatumah (a primary source of tumah) or not:
It became tamei through an av hatumah - whether it became tamei inside or outside, it is burned outside, because it contracted tumah from an av hatumah, which is the more severe form.
It became tamei through a v'lad hatumah (a derived form of tumah) - whether it became tamei inside or outside, it is burned inside. Even if it became tamei outside, since it contracted only a v'lad hatumah, it may be burned inside.
The view of Rabbi Akiva:
Rabbi Akiva disagrees and rules that the place where the tumah was contracted is what determines the matter: wherever the meat became tamei, there it is burned. It makes no difference whether it became tamei through an av hatumah or through a v'lad hatumah, and everything depends solely on whether it happened inside or outside - if it became tamei outside, it is burned outside; if it became tamei inside, it is burned inside.
In summary: the previous mishnah made the place of burning depend on the combination of two conditions - tumah and leaving its designated place; Rabbi Eliezer makes it depend on the severity of the tumah, whether it was an av hatumah (outside) or a v'lad hatumah (inside); and Rabbi Akiva makes it depend solely on the place where the meat became tamei - there it is burned.