The first perek of Massekhet Zevaḥim deals with one main issue: situations where a sacrifice was brought properly, that is, all of the required actions were done according to the law, but improper thoughts were made at the time that the sacrifice was brought. According to the Mishna, there is a Biblical prohibition against such thoughts, but we need to examine the impact that such thoughts will have on the sacrifice and its validity.
The first Mishna teaches that if a sacrifice were brought she-lo li-shmah – with the wrong intention in mind, e.g. the animal had been set aside for one type of sacrifice but was slaughtered for a different sacrifice – it remains a valid sacrifice, although it does not count and the owner will need to bring another sacrifice to fulfill his obligation.
In the Gemara, Ravina quotes Rava as teaching that the Mishna implies that the sacrifice is not sufficient because he had the wrong intention. If, however, he did not have any specific intention, then the sacrifice would work. Rava contrasts this with the law regarding a divorce, where the requirement is that the divorce be written li-shmah – with specific intent for the man and woman who are getting divorced. In the case of divorce, if there was no specific intent, the geṭ – the divorce document – will not be valid.
Rava explains the difference as follows. In the case of sacrifices, the animal has been consecrated already, so a lack of specific intent would leave it in its current situation, as a valid sacrifice. In the case of divorce, however, we do not assume that a married woman is to be divorced, so without specific intent, the geṭ will have no meaning.
Ultimately both the sacrifice and the divorce document need intent. The difference between them is that the intent has already been determined in the case of the sacrifice, and it will remain in place so long as no one changes the situation, as opposed to writing a divorce, where without specific intent, the document does not relate to the woman involved.