Pesach celebrates the Israelites flight from the oppressive Pharoah of Egypt. The Israelites had come to be in Egypt through Joseph, who was an advsior to one of the Pharoahs. However, generations later, the Israelites were enslaved, and forced to build. The Pharoah ordered that every Jewish male born should be drowned, for he feared an uprising. Moses was one of the children who was hidden from this death, and he grew up to lead the Israelites out of Egypt.
The most memorable part of Pesach is the Ten Plagues, culminating in the death of the first born children in all of Egypt. Only those who had sacrificed a ram and had smeared the blood round their doorposts would be saved from the Angel of Death which passed over (hence Passover), which is what Moses instructed all the Israelites to do.
A service is held in the home called the Seder (derived from the Hebrew root for Order, as in order of the service), in which we recall the story of the Exodus, although it should be read so that we ourselves feel as though we were there in the Exodus. During the service, we are instructed to recline in our chairs, to remind us of the freedom we now possess.
On the second night of Pesach (the festival lasts for 8 days), we start counting the Omer.