While giving Israel instructions on how to prepare for their freedom during the final 10th curse (the Passover). God also adds that this day was to be celebrated as an annual holiday (truly, a holy day):
Exodus
12:14
"This is a day you
are to commemorate; for the generations to come you shall celebrate it as a festival to the
Lord-a lasting ordinance."
He says it was to be celebrated by eating unleavened bread for 7 days: beginning on the evening of the 14th day of the first month until the evening of the 21st month:
Exodus 12:18
"In the first month you are to eat bread made without yeast, from the evening of the fourteenth day until the evening of the twenty-first day."
On the first day, all leavening was to be removed from the home, and a sacred assembly in honor of the first day was to be held then the last 7th day have another sacred assembly. Both of these special days were to be days when no work was to be done (days of rest: the only thing that could be done is cook food to be eaten):
Exodus 12:15-16
"For seven days you are to eat bread made without yeast....On the first day hold a sacred assembly...[and] remove the yeast from your houses...and another one on the seventh day. Do no work at all on these days, except to prepare food for everyone to eat; that is all you may do."
God called these seven holy days 'The Festival of Unleavened Bread' because it (specifically the first day) was to be celebrated for the day God would free Israel from Egypt:
Exodus 12:17
"Celebrate the Festival of Unleavened Bread, because it was on this very day that I brought your divisions out of Egypt."
So that night, the Israelites went inside their houses and ate the lamb with unleavened bread and bitter herbs exactly as God desired for them to eat for that Passover night (the first evening/night to eat only unleavened bread).
That night, the 10th curse freed Israel, and the next day as they were being driven out by the terrified Egyptians they left with all their possessions but also left with unleavened bread dough to eat on their journey because they were being driven out so fast:
Exodus 12:31-39
"...the people took their dough before the yeast was added, and carried it on their shoulders in kneading troughs wrapped in clothing....The dough was without yeast because they had been driven out of Egypt and did not have time to prepare food for themselves."
Why this seems to have been unintentional; God seems to have hinted before that he actually wanted Israel to not eat any leavened bread at this time.
Once freed, they journeyed to Sukkoth (a place slightly outside of ancient Egypt) and settled down for that night and cooked the unleavened dough and ate unleavened bread as a celebration meal:
Exodus 12:37-39
"The Israelites journeyed from Rameses to Sukkoth. There… With the dough the Israelites had brought from Egypt, they baked loaves of unleavened bread."
Since it was the 15th day of the first month (that is Aviv/Nisan) the day right after the Passover on the 14th evening:
Numbers 33:3
"The Israelites set out from Rameses (a place in Ancient Egypt) on the fifteenth day of the first month, the day after the Passover."
Through Moses, God commanded Israel to honor this sacred day with 7 days of eating unleavened bread and getting rid of all leavening in their entire nation:
Exodus 13:3-7
"Then Moses said to the people, 'Commemorate this day, the day you came out of Egypt, out of the land of slavery, because the Lord brought you out of it with a mighty hand. Eat nothing containing yeast. —you are to observe this ceremony in this month: For seven days...Eat unleavened bread during those seven days; nothing with yeast in it is to be seen among you, nor shall any yeast be seen anywhere within your borders.'"
He confirms on the final day (that is, the 21st ) a celebration to God is to be held right before the festival ends:
Exodus 13:6
"...and on the seventh [final] day hold a festival to the Lord."
When their children (sons) asked them why they did all this they were to tell them why: and this festival was to be a constant reminder of obeying God and how they were redeemed them as a nation: they were to celebrated it at this exact time every year on his calendar:
Exodus 13:9-10
"On that day tell your son, 'I do this because of what the Lord did for me when I came out of Egypt.' This observance will be for you like a sign on your hand and a reminder on your forehead that this law of the Lord is to be on your lips. For the Lord brought you out of Egypt with his mighty hand. You must keep this ordinance at the appointed time year after year."
God later officially states that the first day of the festival of unleavened bread starts on the 15th and ends on the 21st :
Leviticus 23:6
"On the fifteenth day of that month the Lord's Festival of Unleavened Bread begins..."
This clarifies the possible confusion that the first day of the festival of unleavened bread begins on the 14th evening along with Passover due to God commanding Israel to stop eating leavened bread and begin eating unleavened bread at that time as well.
However, this confirms that's not the case: God just commanded Israel to stop eating leavened bread by the 14th evening when Passover began, but he states that the 14th evening itself is not the first day of the festival of unleavened bread: The next day is.
So while deeply connected to Eachother, Passover and the festival of unleavened bread are separate days/holidays. While speaking of these two first and important holidays God also added another holiday inside of the festival of unleavened bread called The day of waved first fruits (coming soon).