If a person has improper intent when doing the zerikah, the throwing of the blood, that could make the korban (sacrifice) invalid. When dealing with korbanot, most of them have the blood put on more than one spot of the Mizbeach (altar). But not all of those applications are super necessary. They're mitzvah. You're supposed to do them. But even if, let's say, a person does one of them, as we'll elaborate on in the Mishnah, the korban would still be valid. So here, the Mishnah is going to talk about how they are essential and how that would affect the laws of pigul (disqualification due to improper intent).
The Mishnah says: We are talking about all korbanot whose blood is put on the outer Mizbeach. If a Kohen (priest) made only one application of blood, if you only put the blood in one spot, he has attained kapara (atonement) for the owner. Even with one application of blood, when talking about the korbanot that are done on the outer Mizbeach, that is enough, even though generally two corners of the Mizbeach have blood applied to them. If blood was applied to only one of them, that is considered enough. And when we're dealing with the korban hatat (sin offering), where the blood is put on all four corners of the outer Mizbeach, you need two applications in order to make the korban valid. That's how Beit Shammai (House of Shammai) learns it out through the pesukim (verses). Beit Hillel (House of Hillel) argues against that last point and says that even in a case of a korban hatat, where normally all four corners of the Mizbeach have blood applied to them, if blood is applied to only one of the corners, that is still considered a situation where the owner of the korban has received kapara, and the korban is valid.
Now we can apply that to the laws of pigul. If a Kohen made the first application of blood properly, his kavanot were all okay; he had the proper intentions. The second application of blood was done with a problematic intention: that he was going to either partake of the meat or burn the imurim (sacrificial portions) past the time. So while he was putting the blood on the second corner, he had an improper thought. We say he has still attained kapara for the owner, because the korban is not pigul. The korban is completely valid at the moment he puts the blood on the first corner, and the meat and the imurim become permitted right at that time. So even though he had an improper intention afterward on the second corner, that improper intention doesn't do anything because the korban is valid as long as that first corner was done properly. If he made the first application of blood with the intention to eat the korban past its time, and the second application with the intention to eat it outside of its place, then, in that type of situation, it's considered to be pigul, and a person is liable for karet (excision) if he ends up eating the korban.
Even over here, a person who has kavanah to eat the korban outside of its place would usually prevent pigul from kicking in, because the korban would have been invalid for a separate reason. Here, it's different, because the intention about eating it in a different spot was only on the second application of blood, on the second spot where he placed the blood. On the first place where he put the blood, he had an improper intention about eating the korban during the time, and therefore pigul kicked in. What we're saying, basically, is that the application of the first corner is the most essential, and whatever kavanah he has over there determines whether the korban is valid or invalid, and it can affect the status of the korban in a big way.
So, in this last case, regarding pigul, the issue is improper intention about eating the korban or offering the imurim. When he had an improper intention at the first corner about chutz lizmano, about eating the korban past the proper time, it's pigul right away. Even though afterward he had an improper intention about the spot, about eating it outside its spot, which would usually undo pigul, here that happened afterward, at the second corner, and pigul was already intact by the first corner. We say that this korban is pigul, and if a person ate a korban, he would be hayav (liable) karet.