There is a kabbalic concept known as the "ten crowns of impurity". Thus we lay down ten pieces of chametz to represent those ten crowns. See R. Zev Wolf haLevi of Zitomir, Ohr haMeir (vaYikra: Pesach), quoting Arizal in Pri Etz Chaim (Mitzvos, end of ch. 4).
(It is well known that the removal of chametz from our homes symbolizes the removal of the Evil Inclination from within us, and our tradition frequently refers to the E"I as the "yeast in the dough". The candle of Bedikas Chametz symbolizes the searching of the soul for traces of spiritual chametz. See e.g. Yalkut Zapania 567 and Zohar Parshat Bo.)
For another source for this custom, see Tzitz Eliezer (9:17:9).