Specifically, it celebrates the last of the ten plagues that God sent on to Egypt, in order to force the Pharaoh to allow the Israelites to depart from slavery.
God sent the Angel of Death to kill the first–born sons of the Egyptians. He told Moses to order the Israelite families to sacrifice a lamb and smear the blood on the door of their houses, so that the angel would know to 'pass over' the houses of the Israelites.
Wikipedia tells how (according to the Bible), following the Passover, "Pharaoh order[ed] the Israelites to leave, taking whatever they want[ed], and ask[ed] Moses to bless him in the name of the Lord."
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