Leavening is something put in bread dough or cakes to make it puff up and bake up nice and soft. It includes anything that contains yeast or rises. In the very same way, the examples of pride, arrogance, alcohol and drug abuse puff us up and turn even the strongest people soft and weak. When we choose our own way over God's way we leave ourselves to our own defense, a very precarious place indeed. 1st Corinthians 5:7 says: Don't you know that a little yeast works through the whole dough? Get rid of the old yeast that you may be a new batch without yeast, as you really are. For Messiah, our Passover lamb has been sacrificed.
Removing the leavening from the house is a monumental task, symbolizing how difficult it can be to get the sin out of one's life. The night before Pesach, we do a ceremonial search for leaven, called checking for leaven ("bedikat hametz") that can be a fun time involving the children with the flashlights and prizes. The next morning we destroy the leaven ("biur hametz"). We must get rid of all leaven in our possession by selling, burning or throwing it into the wind.
During Pesach and the Feast of Unleavened Bread, it is forbidden to eat leavened bread throughout the celebration. As the children of Israel fled from Egypt, they didn't have time for their dough to rise. Instead the hot desert sun baked it flat. We stay away from eating leavening in all our food for the entire eight days of the feasts. It's so we understand and remember the careful planning and work we need to do in order to keep sin out of our lives. Our kitchen and house are cleaned very carefully before the celebration to get all the crumbs of leavening out of our life. We do this so we understand and remember how easily the little crumbs of sins build up and maybe even go unnoticed.