Most of the Korbanot (offerings) have their blood thrown on the outer Mizbeach (altar) in the Chatzer, the courtyard of the Beit HaMikdash. The exception is the Korban Chatat (sin offering), whose blood is applied inside the Heichal, the sanctuary building. The Mishnah here is going to discuss what happens if the blood of an outer Korban is mixed with blood from something like the Korban Chatat, whose blood is applied on the inner Mizbeach.
The Mishnah says that if blood that is supposed to be applied inside the Heichal, on the inner Mizbeach, is mixed with blood that is applied on the outer Mizbeach, outside the Heichal in the courtyard, you are not allowed to use the mixture at all. You cannot apply blood that is supposed to go in one spot in another spot. It specifically has to go on a certain Mizbeach, so the mixture becomes a problem for both the inner Mizbeach and the outer Mizbeach. You cannot apply it when blood from another Korban is mixed with the blood that is supposed to be applied there. Therefore, you should pour it into the channel of water that runs out of the Beit HaMikdash.
But if the Kohen (priest) acted against the Halakha (Jewish law) and applied the mixture outside and then inside, each Korban would be valid, because we would say that each Korban had its blood put on the correct Mizbeach. There was other blood mixed with it that was incorrectly applied, but the bottom line is that each Korban was applied to the correct Mizbeach in some sense, so it would be a valid Korban.
But if he did the opposite—if he applied the mixture inside the Heichal and then outside—the one applied first, the inner Korban, would be valid after the fact. But there is a Machloket (dispute) about the outer offering, the one that is brought. In the end, Rabbi Akiva posel (disqualifies): Rabbi Akiva says the outer offering is invalid, but the Hachamim (Sages) say that in these cases it would normally be valid.
What is the Machloket about? It is based on a Pasuk (verse) that tells us that if the blood of an ordinary Chatat is brought inside the Heichal, the Korban becomes invalid. As we mentioned earlier in the introduction to this Mishnah, certain types of Chatat offerings are brought inside, to the Heichal, where the blood is applied to the inner Mizbeach. Those are different types of Korban Chatat. But the blood of the ordinary Korban Chatat is applied outside, and a Pasuk explicitly says that you cannot bring the blood inside, or the Korban becomes invalid.
So the question is whether this Halakha applies only to the ordinary Chatat or to all the outer Korbanot as well. For example, if you have a Korban that is supposed to be brought outside, but I bring the blood inside the Heichal, is that a problem or not? It is definitely a problem with the ordinary Korban Chatat. So the question is how that applies more broadly.
Rabbi Akiva says that any blood of an outer offering that is supposed to be brought on the Mizbeach in the Chatzer, the courtyard of the Beit HaMikdash, and is not supposed to be brought inside the Heichal, makes the Korban invalid if it is brought into the Heichal. When the Torah disqualifies blood brought inside the Heichal, this does not apply only to the ordinary Korban Chatat; it applies to all Korbanot that are supposed to be brought outside the Heichal, everything that is supposed to be applied in the Chatzer. Therefore, as soon as the mixture was brought inside, and then outside, it automatically became Pasul (invalid). The outer offering in this situation becomes invalid.
Just to remember the case again: the person brought the blood inside, applied it, and then went outside. So even though he applied it on the proper Mizbeach in the end, outside, there is a problem: he first brought the blood inside the Heichal, inside the sanctuary, and by doing that, the outer Korban became invalid.
Hachamim omrim, Chatat bilvad (the Sages say: only a sin offering). The Hachamim argue with Rabbi Akiva and say that when the Torah tells us that a Korban Chatat offered outside cannot be brought inside, that is talking only about the Chatat, not other Korbanot. Therefore, in this situation, if the blood of the ordinary Chatat was brought inside the Heichal and then brought outside to be applied on the Mizbeach, the Chatat would become invalid. But if any other type of outer offering was brought inside, the Korban would remain acceptable for the Avoda (Temple service) once it was brought outside. The fact that it was brought inside does not invalidate anything, and the outer offering is valid once it is put on the Mizbeach.
The next Tanna (Mishnaic sage) is going to disagree with the opinion of the Hachamim and say that when the Pasuk talks about the outer Chatat, the disqualification also applies to one other type of outer offering. The Hachamim say it applies only to the outer Chatat. Reb Eliezer says it applies to all Korbanot that are brought outside. Reb Eliezer is going to say it applies to the Chatat plus one. He says that not only is the Chatat subject to this type of disqualification, but the Asham (guilt offering) is as well, as the Pasuk tells us. According to Reb Eliezer, the disqualification applies to the ordinary Chatat and to the Asham as well, compared to the Chatat and the Asham. But the prohibition would not apply to any other type of outer offering.