Generally speaking someone who is tameh – has become ritually defiled by contact -cannot participate in the Temple service in any way. There is, however, an exception: the case of tumah hutrah be-tzibur – if the majority of the Jewish people are tameh, then the sacrificial service can take place, performed by kohanim who themselves are tameh.
Most of our daf is devoted to an examination of the disagreement between Rav Nahman and Rav Sheshet with regard to the question of tumah hutrah be-tzibur – how to understand the rule permitting sacrifices to be brought when the majority of the community is tameh. Rav Nahman explains that tumah hutrah be-tzibur means that the rules of tumah simply do not apply under these unusual circumstances. According to Rav Sheshet, however, the rule is really that tumah dehuyah be-tzibur – not that the Torah totally permits it, rather that the need to bring sacrifices in this case “pushes aside” the existing prohibition about tumah, even as the prohibition remains.
To explain this concept, it is important to note that the question of hutrah (permitted) vs. dehuyah (pushed aside) is not unique to questions about ritual purity in the Temple and its sacrifices. We find a similar discussion with regard to the rules of Shabbat, when a number of different circumstances will permit melakhot – activities on Shabbat – that are, ordinarily, forbidden.
Regarding Shabbat we find that approaches differ based on the reason that the activity needs to be done. When communal sacrifices are brought in the Temple on Shabbat it is clear that Shabbat is hutrah. Such activities are totally permitted. On the other hand, potential life-and-death situations, when we certainly will allow activities to be done on Shabbat to save the individual, are likely considered dehuyah. It is thus important to limit activities to those melakhot that are essential, and anything that can be done without transgressing forbidden activities on Shabbat should be done in that way (see Shulhan Arukh Orah Hayyim 328 for a discussion of these issues).