Actually, that is a very good question, I'll try to give an equally good answer here...
Rather than do a verse by verse of the entire chapter, let's examine the key verses and then you can read the chapter at your leisure...
Exo 12:6 And ye shall keep it up until the fourteenth day of the same month: and the whole assembly of the congregation of Israel shall kill it in the evening.
Exo 12:7 And they shall take of the blood, and strike it on the two side posts and on the upper door post of the houses, wherein they shall eat it.
So here we see the Passover lamb, kept from the 10th day of the month and then killed on the 14th at evening. The blood was put on the doorway of the house. If not there, the death angel was coming in. Symbolic today of Christ's blood on the entrance to our heart/mind and the protection from the wages of sin (death).
Exo 12:14 And this day shall be unto you for a memorial; and ye shall keep it a feast to the LORD throughout your generations; ye shall keep it a feast by an ordinance for ever.
While it is an ordinance forever, the application has changed under the New Covenant...
Mat 26:26 And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body.
Mat 26:27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;
Mat 26:28 For this is my blood of the new testament, which is shed for many for the remission of sins.
Mat 26:29 But I say unto you, I will not drink henceforth of this fruit of the vine, until that day when I drink it new with you in my Father's kingdom.
Joh 13:2 And supper being ended, the devil having now put into the heart of Judas Iscariot, Simon's son, to betray him;
they had eaten the traditional Passover, Christ then instituted the foot washing ceremony and then the bread and wine. You can read John 13 and see this ceremony added to the bread and wine as the New Covenant Passover ceremony.
Anyhoo, back to Ex 12 and we see a change from the Passover to the Days of Unleavened Bread...
Exo 12:15 Seven days shall ye eat unleavened bread; even the first day ye shall put away leaven out of your houses: for whosoever eateth leavened bread from the first day until the seventh day, that soul shall be cut off from Israel.
Exo 12:16 And in the first day there shall be an holy convocation, and in the seventh day there shall be an holy convocation to you; no manner of work shall be done in them, save that which every man must eat, that only may be done of you.
Exo 12:17 And ye shall observe the feast of unleavened bread; for in this selfsame day have I brought your armies out of the land of Egypt: therefore shall ye observe this day in your generations by an ordinance for ever.
Exo 12:18 In the first month, on the fourteenth day of the month at even, ye shall eat unleavened bread, until the one and twentieth day of the month at even.
Exo 12:19 Seven days shall there be no leaven found in your houses: for whosoever eateth that which is leavened, even that soul shall be cut off from the congregation of Israel, whether he be a stranger, or born in the land.
Exo 12:20 Ye shall eat nothing leavened; in all your habitations shall ye eat unleavened bread.
Why isn't the Passover the First Day of the seven Days of UB?
Lev 23:5 In the fourteenth day of the first month at even is the LORD'S passover.
Passover is the 14th but the First Day of UB is not until the 15th...
Lev 23:6 And on the fifteenth day of the same month is the feast of unleavened bread unto the LORD: seven days ye must eat unleavened bread.
Back to Ex 12...
Exo 12:36 And the LORD gave the people favour in the sight of the Egyptians, so that they lent unto them such things as they required. And they spoiled the Egyptians.
Exo 12:37 And the children of Israel journeyed from Rameses to Succoth, about six hundred thousand on foot that were men, beside children.
Exo 12:38 And a mixed multitude went up also with them; and flocks, and herds, even very much cattle.
Exo 12:39 And they baked unleavened cakes of the dough which they brought forth out of Egypt, for it was not leavened; because they were thrust out of Egypt, and could not tarry, neither had they prepared for themselves any victual.
This explains Israel leaving Egypt. One thing to note is that they left AT NIGHT...
Deu 16:1 Observe the month of Abib, and keep the passover unto the LORD thy God: for in the month of Abib
the LORD thy God brought thee forth out of Egypt by night.
This could not have been the night of the Passover. They were not immune to the death angel and had they been outside their homes (out from under the blood of the lamb) the firstborn would have died just like the Egyptians.
Exo 12:40 Now the sojourning of the children of Israel, who dwelt in Egypt, was four hundred and thirty years.
Exo 12:41 And it came to pass at the end of the four hundred and thirty years, even the selfsame day it came to pass,
that all the hosts of the LORD went out from the land of Egypt.
Exo 12:42 It is a night to be much observed unto the LORD for bringing them out from the land of Egypt: this is that night of the LORD to be observed of all the children of Israel in their generations.
Verse 41 shows this was not the Passover night or the firstborn would have died. Ex 12 goes from the evening of the Passover to the Days of Unleavened bread, back and forth.