In Chapter 2, Mishnah 3, the Mishnah continues and expands upon what was explained in the previous Mishnah, distinguishing between two invalidating thoughts: the thought of outside its time, the result of which is potential piggul, and the thought of outside its place, which merely invalidates the offering.
The language of the Mishnah - the four services:
The Mishnah opens: "Zeh hakelal" - this is the rule, and enumerates the services during which an improper thought invalidates:
Slaughtering.
Receiving the blood.
Conveying the blood to the altar.
Sprinkling the blood on the altar.
We are speaking of a case where, at the time of performing one of these four services, it was accompanied by an invalidating thought, and the thought was directed at something designated for that purpose:
"Leechol davar shedarko leechol" - to eat something that is normally eaten, referring to the meat designated for consumption, as opposed to the imurim.
"Lehaktir davar shedarko lehaktir" - to burn something that is normally burned, referring to the general imurim, which are normally offered up on the altar.
This is to exclude a situation where he thought to eat the imurim or the like, or to offer upon the altar meat that is designated for consumption and not for burning.
Two thoughts and two outcomes:
Outside its place: He thought to perform the burning or the eating in the wrong place, outside the Temple or the like - the offering is invalidated, and one who eats from it does not incur the separate punishment of kares (spiritual excision by Heaven).
Outside its time: He thought during one of the four stages to burn the imurim or eat the meat outside of its proper time, after the designated time for their burning or eating has passed - the offering becomes piggul, which is a more severe invalidation, and one who eats from it incurs kares.
"Uvilvad sheyikrav hamatir kemitzvato" - provided that the permitting portion is offered in accordance with its commandment:
This is an important condition, which serves as an introduction to the next Mishnah: The permitting portion must be offered according to its halachah, just as we were commanded to offer it. The meaning of the condition, not from the simple reading of the text but from the underlying concept, is that if the thought of outside its time was accompanied by an additional invalidating thought, the problem is no longer pure, but rather mixed with another thought.
For example: A person offers a chatas, and not only did he think to eat it outside its time, but he also slaughtered it for the sake of an olah - meaning, a thought of not for its own sake was added here. In such a case, the thought is not pure, and therefore, even though the offering is certainly invalid, it does not carry with it the law of piggul and the liability of kares for one who eats from it.
In summary: The law of piggul applies only when the intention is exclusively for outside its proper time, without any other invalidating intention mixed in; and the punishment of kares exists only in this pure case of outside its proper time.