When the Temple stood, there was a mitzva to make a pilgrimage three times a year, once on each festival, and to offer an ola and shelamim on the first day of the festival. These offerings were referred to as olat re’iya and shalmei ḥagiga. One who did not offer them on the first day could fulfill his obligation to do so up through the conclusion of the festival, meaning the seventh day of Pesaḥ or until Shemini Atzeret (Ḥagiga 9a). One who did not offer them on Shavu’ot could offer them in the following six days. Just as one had seven days to bring the ola and shelamim for Pesaḥ, so too one had a week to bring them for Shavu’ot (Ḥagiga 17a).
Since these festival sacrifices may be offered during the six days following Shavu’ot, an element of festival joy continues as well. Therefore, the custom is not to say Taḥanun during that time (MA; MB 131:37).
On the day after Shavu’ot, known as Isru Ḥag, fasting and eulogizing are prohibited. This is because it is “a day of slaughter,” meaning a day when sacrifices are sometimes brought. Specifically, when Shavu’ot was on Shabbat, the olat re’iya and shalmei ḥagiga would be postponed until Sunday, which was Isru Ḥag. Additionally, even when Shavu’ot was not on Shabbat, there were always many people who did not get a chance to offer all their sacrifices on the festival. What they did not manage to offer on Shavu’ot, they would offer the next day. A day on which sacrifices are offered is considered a day of simḥa. Therefore, one may not fast then (SA 494:3; Levush; MA ad loc. 3; SAH ad loc. 19; see above 2:13).