Many people have the practice after the end of Pesach not to immediately eat the Hametz in their homes which they had sold to a gentile, and to instead wait until the Rabbi through whom they had sold the Hametz purchases the Hametz back from the gentile. In truth, however, this is not necessary. When the gentile purchases the Hametz before Pesach, he makes a small down payment, committing to pay the full price later, after Pesach, but of course, the Hametz is then purchased back from the gentile right after Pesach. Most sale contracts used by Rabbis today include a clause stating that if some of the sold Hametz is eaten after Pesach, the value of that Hametz will simply be deducted from the amount which the gentile legally owes. Therefore, Hacham Bension Abba Shaul (Israel, 1924-1998) writes (listen to audio recording for precise citation) that one may make use of the Hametz immediately after the conclusion of Pesach, and does not have to wait for the Rabbi to purchase the Hametz back from the gentile.
Hacham Bension adds that if this clause was not included in the contract, then one should wait before using his Hametz until the Rabbi purchases the Hametz back from the non-Jew. Other Poskim, however, maintain that even in the absence of an explicit cause, it can be assumed that the gentile who owns the Hametz does not mind if the Jew partakes of some of the Hametz, the value of which will be then deducted from the amount he needs to pay.
In Israel, one should not eat Hametz until 72 minutes past sundown on the last day of Pesach. Since eating Hametz on Pesach constitutes a Torah prohibition, it is proper not to eat Hametz until the final day of Pesach has ended even according to the view of Rabbenu Tam (France, 1100-1171), who maintained that the Halachic day ends only 72 minutes after sunset. Outside Israel, where an additional day of Yom Tov is observed by force of Rabbinic enactment, this is not necessary, since on this extra day, eating Hametz is not forbidden by Torah law. As soon as the Yom Tob ends, one may partake of the Hametz.
Summary: Some people have the practice the night after Pesach ends to refrain from eating the Hametz they had sold, until the Rabbi buys the Hametz back from the non-Jew. Strictly speaking, however, this is not necessary. In Israel, one should refrain from Hametz on the final day of Pesach until 72 minutes after sundown.