The Passover Preparation
Central to the Passover story is the Passover, or paschal, lamb. In Exodus 12:1-13, the Israelites are instructed to take a young lamb, a year-old male, and to slaughter it at twilight before the Passover. Over time, this becomes known as "Preparation Day."
They are then instructed to take some hyssop, dip it in the blood from the lamb, and cover with blood their doorposts and the lintels of their homes. This blood becomes the protection for the Israelites when the destroyer comes to strike down all the firstborn; he will see the blood on the doorframe and "pass over" that home, sparing all inside. Significantly this is the only plague of the 10 where the Israelites are required to take any action on their own behalf.
The Passover Lamb of God
In the Gospel of John, Jesus is explicitly connected to the Passover Lamb. When John the Baptist first encounters Jesus in that Gospel, he exclaims, "Here is the Lamb of God, who takes away the sin of the world!" (See John 1:19-34). That proclamation continues to reverberate throughout the Gospel. Jesus is crucified in John on "the Day of Preparation" (John 19:14), the same day upon which the lambs would be sacrificed. As he hangs on the cross, a branch of hyssop is used to covey a sponge of vinegar to Jesus' lips (John 19:29). Again and again, we are reminded in John that Jesus fulfills the role of the Passover lamb; through his blood on our lives, we are spared from death. Jesus' death on the cross causes Death to "pass over" us forever.
Like the plague of Passover, this salvation is the gracious act of God; we cannot earn it. However, also like the Passover, this salvation does require our response and acceptance. We cannot make the destroyer pass us by; but we must cover the doorframes of our hearts with his life's blood to be saved.
Extras
The term "Agnus Dei" has become famous in Christian art and music. The painting above of the lamb prepared for slaughter is called "Agnus Dei" and was painted by Francisco de Zurbaran around 1635, for example. Contemporary Christian music and hymns often use this title as well. It is simply Latin for "Lamb of God."
In the Book of Revelation, John sees "a Lamb, looking as if it had been slain, standing in the center of the throne" of God (Revelation 5:6). This is the title that Jesus retains for the rest of Revelation 5 and 6. There is a powerful and fascinating dichotomy from the "Lion of Judah" and the "Lamb of God," and yet both titles are used in this same passage to refer to Jesus. Jesus' identification with the Passover Lamb stretches even to Revelation and heaven itself.