The last plague that God sent was death to the firstborn son of every family in Egypt.  The only way to escape the "death angel" was to follow a specific procedure set by God Himself.

You found a perfect male lamb.  On the evening before this death decree was to occur, you killed the lamb, roasted it on an open fire, took the blood and smeared it on the sides of the front door.  Then you ate all of the meat, and burned anything that was left over.

You dressed all the family so that they would be ready to leave Egypt early the next morning.  Every one slept in their clothes--if they could sleep at all.  The only provision you took with you was unleavened bread.  (So it wouldn't mold.)  And then, amid the screams of the Egyptians--who had ignored God's warning--who were reacting to the death of their children, you fled for your lives.

Life is the most precious thing in the world.  And the concept of sacrificing one life for another's sin is first mentioned in Genesis.  It is our oldest written record.  The entire account leads up to the ultimate sacrifice for sin:  Jesus.

Adam and Eve:  God sacrificed an animal to cover their nakedness when they disobeyed him.
Cain and Abel:  Abel followed directions for a blood sacrifice.  Cain didn't and was punished.
Noah: Offered a burnt offering of every clean beast when they were once again on dry land.
Abraham: Obeyed God, willing to sacrifice Isaac.  But in the first picture of substitution, God spared Abraham's son and said: "My son, God will provide for Himself the lamb for a burnt offering."

Which God did for us.  Sending His own son as a substitute lamb.  A Lamb that takes away the sin of the world.  Life.  The most precious sacrifice.  "No greater love has any man than to lay down his life for his brother."

The Passover dates to the Exodus event.  And now we commemorate when we: "Take, eat.  This is my body.  Do this in remembrance of me."  He is our passover Lamb.  He is our sacrifice for our sin.  He laid down His body for you and me.  That's sacrifice.