”Kosher,” from the Hebrew word for “proper” or “pure,” is the system of dietary rules in Judaism; there’s a level of additional rules for Passover. Over the seven or eight (depending on who’s counting) days of Passover, many Jews will go “kosher for Passover” by avoiding most grain products.
Observant Jews may make an effort, before Passover begins, to throw all the grains out of their house and clean it thoroughly. But many less observant Jews — even Jews who don’t keep kosher the rest of the year — will observe the Passover restrictions. In addition to observing tradition for its own sake, going kosher for Passover can serve a function almost like the one Lent serves for Christians during this time: a reminder of the sacrifices of past generations, and a lesson that freedom sometimes requires sacrifice.
The main exception from the ban on eating grain products is matzah — the crackerlike, unleavened (yeastless) bread that is the most traditional Passover food. The original Passover story says that when the Jews were fleeing Egypt, they were scrambling to make food for the journey and didn’t have time to let bread rise, so they made matzah as a quick alternative. The practice of eating matzah commemorates the hardship of the flight.
In recent decades, Jewish food manufacturers have made kosher-for-Passover varieties of all kinds of things, from granola to cake mix. (This makes for substantially less hardship.)
The rules for Jews whose families are from Eastern Europe or Russia (called “Ashkenazic Jews”) have a few extra restrictions; Jews from Spain and the Mediterranean (called “Sephardic Jews”) don’t. Their interpretations of Kosher for Passover diverged during their many centuries apart.