Bitul and Biur
The laws of Pesach include many Torah laws as well as Rabbinic laws. The Torah uses the word, תשביתו, as the instruction to get rid of our Chametz during Pesach.
There are two methods of disposing of our Chametz. The first is referred to as “Bitul,” or nullification. This is done by making a declaration that we no longer own any Chametz in our possession. It is “Hefker,” or ownerless. This intent is all that is necessary on a biblical level.
The second method of תשביתו, would be “ביעור,” or the burning of Chametz. The Chametz is destroyed to the point that no benefit can be derived from it.
The Rabbis require that we do both ביטול and ביעור. The reason for this, is the concern that one will not renounce his Chametz with a full heart, because of its financial value.
The custom to search for Chametz, known as בדיקת חמץ, and the selling of Chametz, מכירת חמץ, to a local rabbi, are both Rabbinical in nature.