Before Passover begins, many Jews have already begun their holiday observance in a flurry of preparations. Preparing for Passover includes both a literal house cleaning and a ritual one. Traditional Jews remove any foods that are leavened or fermented, like bread, vinegar or beer, or that contain any ingredients that could be made into something fermented, like flour. By searching for and removing all the leavened foods, such as bread, pasta and crackers (called "hametz" in Hebrew), traditional Jews ready their kitchens for the Passover foods they will eat at the seder and the rest of the week of Passover.
Some families try not to have any hametz at all in their possession. One way to do this is to plan ahead and eat up all the leavened food before the cleaning begins, or to donate sealed-up packages of hametz to food banks. Since food is expensive and Passover is only one week long, some Jewish families sell any unused portions of leavened products to neighbors who aren’t Jewish, and then buy them back after the holiday. That way, the hametz isn't technically in their possession, even though they are actually storing it in sealed-up boxes in the basement, and even though they sold the food for some tiny amount of pocket change. Some congregations use the legal fiction of the hametz "sale" as an excuse to give money to tzedakah: they deputize their rabbi to sell the food for them, and give him or her a check to be their agent. The rabbi sells the leavened food to non-Jews and donates the agent money to charity.
After the householders have cleaned thoroughly, they may perform a ritual called bidikat hametz, the Search for Leavening. In this ritual, one person hides 10 bread crumbs throughout the house and then the family searches for them by candlelight, using a feather to scoop them into a paper cone or envelope, and taking them outside and burning the whole thing (feather and all) with the inclusion of a wooden spoon or stick to make sure the fire lasts long enough to consume the crumbs. If you want to try this ritual, you can see more detailed instructions at this site.
Removing the hametz is a symbolic way to remind us to pay to attention to aspects of our character that have become inflated, like pride and vanity. Some use this ritual to think about what the metaphorical hametz is in their lives, and to take the opportunity to cleanse themselves of it. As they search for the ten pieces of bread spread through all the rooms of the home, they can also look into all the corners of their lives and leave no hidden parts of themselves unexamined. The act of removing the leavening can also help us give away the objects that we have accumulated that might benefit others, like extra winter clothing or towels and blankets and toys. Along with the literal benefits of regular thorough house cleaning, this is also an opportunity to engage the whole family in thinking through this ritual and their lives.
In modern Jewish lives, removal of the packaged hametz may be stored in the basement or in a cabinet with tape over it saying "do not touch until after Passover". Some Jewish families don't perform the ritual of removing hametz, and some only "Keep Passover" for the seder meal. There is no ritual or proscription in Judaism that is followed by everyone, nor are they followed the same way in every home and every year. If you're a guest, it is always best to ask your host what their traditions are and how you might help to keep those traditions when you are preparing to arrive.
The Guide to Passover for Interfaith Families is also available in PDF and Word formats.