Unlike the other major holidays on the Jewish calendar, the holiday of Shavuot lasts only two days (one day in Israel). However, Shavuot is followed by six "days of fulfillment" during which the holiday offerings can be brought, for those who did not manage to bring them during the holiday itself.
Some offerings are not allowed to be brought on the holiday itself; this includes private offerings that are entirely burnt on the altar. According to the opinion of the school of Shammai, such offerings are forbidden to slaughter on the holiday. For this reason, the day following the holiday became known as the "day of slaughter" -- during which offerings could be brought.
As a result of this practice, an interesting halachah (law) developed: In the event that the Holy Temple is not yet rebuilt by Shavuot, but it is built during the "days of fulfillment," we will be obligated to bring all the holiday offerings during that period. Since we were unable to bring the offerings on Shavuot itself, we will be obligated to bring them during the days of fulfillment.
However, during exile all of us are considered impure as a result of contact with the dead. After Moshiach's coming we will all need to be purified with the ashes of a red heifer. This process will take seven days, after which the "days of fulfillment" will have already passed.
The solution, though, is simple. When the Temple is rebuilt, the righteous will immediately be resurrected, including Aaron and his sons, who will be free of impurity. They will bring all the required offerings in the Temple on behalf of the Jewish people.