Exodus 12 - 13
God flips the Hebrew calendar, making the 7 th month (Nisan - also called Abib) now the 1 st month, and provides instructions to them in advance of the first Passover. A spotless lamb is to be taken for each household on the 10th of the month, inspected for several days (for purity), and then slain on the 14th , with the blood to be painted on the doorposts and lintel of each house. Unleavened bread is to be eaten for 7 days, from the 14th through the 21st .
The Lord slew all first-born males in Egypt that night, but all were spared who had the blood of the lamb on the doorposts of their house. Pharaoh’s own son was killed, and he finally instructs Moses and Aaron to leave, after all of Egypt was (essentially) destroyed. The Lord instituted the feast of Passover to be celebrated every year thereafter on the 14th day of the first month.
Jesus was crucified on the 14th day of the first month, and became the fulfillment of the type, represented in the first lamb that was slain to save people from the judgement of God.
As Israel goes out from Egypt, God declares that the first-born males in Israel are His, and institutes the feast of Unleavened Bread, which Israel will eat for the next 7 days, due to traveling. God establishes His visible presence in the form of a cloud by day, and a pillar of fire by night, which will lead Israel for the next 40 years.
He also leads them to the Red Sea, rather than taking them Northeast along the sea coast, so that Israelites cannot later turn around and go back.