There were certain customs that Judaism developed over time to deal with the issue of making sure that all the hametz (leaven) was out of the home.
One of the most well known traditions involves searching for hametz by candlelight. It is usually done on the evening of the 13th of Nissan just before the holiday begins. Someone would light a candle (usually a parent) and then get a large feather and a wooden spoon. They would go to a few places in the house with their children to symbolically check for crumbs of bread. 10 pre-planned locations is a traditional number so the kids (searchers) can get the feeling of a good search (parents would make sure there were a couple of crumbs left after cleaning the house thoroughly). When the crumbs could be spotted by the light of the candle the child would sweep the crumbs away using the feather into the spoon. Then the crumbs would be wrapped up and burned on the following morning, the 14th of Nissan.
During the Second Temple times, it was customary for a priest to set out 2 loaves of bread on one of the roofs of the temple where everyone could see. When one loaf was removed, everyone knew they could no longer eat anything with leaven in it. When the other was removed it was a signal to burn the hametz and bonfires were lit all around Jerusalem.(1)
Then there would be a symbolic prayer said.
Today we can find a similar prayer in the Jewish prayer book.
Read what a Nullification Prayer says.
Read more about the Holiday Of Passover
Leaven is often associated with sin in the Bible.
1). The Feast of Israel by Bruce Scott with Friends of Israel Ministries.
The Complete ArtScroll Siddur published by Mesorah Publications, ltd p.655