Here we'll talk about the intentions a person should have when the avodah (service) of a korban (offering) is taking place. Here we're talking about the person who's doing the korban, as opposed to the person who may be bringing the animal in and having it done for him. We're talking about the Kohen (priest) who is sacrificing. The Mishnah says: The animal korban is slaughtered with six different things in mind. Number one, for the sake of that specific type of korban. If it's a korban, the slaughterer has to have in mind that it should be a shelamim (peace offering). Number two, for the sake of the person bringing the korban, for the owner of the korban; the person should have that person in mind. Number three, for the sake of HaKadosh Baruch Hu (The Holy One, blessed be He): that's an offering for Hashem. Number four, for the sake of the fires of the Mizbeach (altar), so that they should burn the korban completely—the parts of the korban that are put on the Mizbeach. It's not there so that, when you put it on the fire, you can just get a small roast out of it and then take it off before it's completely burnt. Rather, if it's going on the Mizbeach, it should be fully put on the Mizbeach.
Number five, for the sake of the smell. The emurim—the limbs and the meat of the olah (burnt offering)—are put on the Mizbeach in order to produce a smell, an aroma. And from there we learn that you're not allowed to roast the korban at all before you put it onto the Mizbeach. The initial burning that happens on the Mizbeach is the one where the fats are dripping off. That's what creates the smell the korban is supposed to have. And if you roast them at all beforehand, you're depriving the Beit HaMikdash of that beautiful smell of the roasting meat, of the burning meat. So that, too, has to have been kept in mind.
Number six, for the sake of bringing pleasure to HaKadosh Baruch Hu. When a person follows the mitzvot (commandments) of Hashem, he, for lack of a better term, kivyachol (as it were), brings enjoyment to HaKadosh Baruch Hu. VehaChatat vehaAsham leshem chet (and the sin offering and the guilt offering for sin). When talking about korban haChatat (sin offering) or korban haAsham (guilt offering), which are brought for Kapparah, as atonement for specific sins that are done, a person has to have Kapparah for those sins in mind as well.
Amar Reb Yosei (Reb Yosei comments over here): af mi shelo hayah belibo leshem echad mikol elu kasher, says Reb Yosei. Even if a person did not have in mind that it should be for the sake of those things, it's still valid, as long as a person did not have a problematic intention in mind that would invalidate the korban. The korban is okay. Shehu tenai Beit Din (rabbinical court), because there was a decree done by the Beit Din in earlier times that a person should not have anything in mind when he's slaughtering the korban, because the korban is for its own sake, so that people should not have an invalidated korban.
The korban here is being done, as we mentioned, by the Kohen. The Kohen has to have very specific intentions in mind. So, Chachamim (the Sages) were nervous that a Kohen would have improper intentions and invalidate the korban, as opposed to having neutral intentions, which would still not bring on any problems. So, he's making two points over here. Number one, if somebody slaughters the korban without these six different intentions, the korban is still valid. We see this from the tenai Beit Din, that Chachamim advised not to have any intentions. And Chachamim, of course, would not tell us to have no intentions if the six intentions that we mentioned earlier are fundamental and essential. So, therefore, we see that having no intention would not invalidate the korban. Therefore, what we see from here, according to Rabbi Yosei, is that a person should have no intentions. She'ein hamachshavah holechet ela achar ha'oved. Chachamim were nervous that the person who was doing the avodah would have the wrong intentions, because his intentions are the ones that matter, as opposed to the owner of the korban. It depends on what he's thinking. So, therefore, if a person was slaughtering the korban—probably the Kohen, because you're also allowed to have someone else do it for you, but it'll probably be a Kohen in this type of scenario—and he had proper intentions, if there was a disconnect between the owner and him, that would invalidate the korban. So, therefore, Chachamim set up this system.