Exodus - Blood on the Doorpost
The Torah describes (Exodus 12:6-7) how each Hebrew family designates a lamb, and sets it aside. On the evening of the Israelites' deliverance from slavery in Egypt, they slaughter the lamb, roast and eat it. The lambs' blood is placed on the doorposts of their houses as a sign that Israelites live in those homes.
The name Passover comes from this offering. When God kills the Egyptian firstborn, He passes over the homes whose doors are smeared with blood.
But can't God tell who's who without a sign?!
The Aish Rabbi Replies:
When oppressed people become free, they are frequently just as brutal as their erstwhile oppressors. It turns out that it is not oppression they objected to. They'd just prefer to be on the other end of the whip.
Society's values implicate us unless we explicitly repudiate them. As a condition of their freedom, God demands that the Hebrews withdraw from Egypt and reject its values.
(This same idea helps explain why Noah had to shut himself up in an ark to escape the flood, and why Lot and his wife were told to run away from Sodom without looking back.)
The Hebrews mark their separation from Egypt by going into their homes, shutting their doors, and marking them with the blood of their offering – a rejection of the Egyptian sheep deity. All of this would serve as a sign of their devotion to God.