How does the Feast of Unleavened Bread point us to Jesus?
At the time of the festival all Jews were to sweep the yeast out of their homes. Thus they would cleanse their homes completely of this stuff, similarly to how deeply we clean dorms and apartments at the end of our leases in order to avoid fines. And several times in Scripture yeast is connected with the growth of evil or the spread of sin. So with this in mind, look with me at 1 Corinthians 5:7-8:
"Cleanse out the old leaven that you may be a new lump, as you really are unleavened. For Christ, our Passover lamb, has been sacrificed. Let us therefore celebrate the festival, not with the old leaven, the leaven of malice and evil, but with the unleavened bread of sincerity and truth."
So we see that Christ is our Passover Lamb, the one whose blood covers the lives of believers and protects them from the angel of death. But then, after people place their trust in Christ for salvation, they are to leave behind their former life of sin, to sweep out the yeast in their lives.
Thus, the feast of unleavened bread is a picture of the Gospel, with Jesus serving as the sacrifice for our sins, and the bread reminding us to let the Spirit make a clean sweep in our lives, getting rid of sin in order to live in true holiness.
How does the Feast of Harvest point us to Jesus?
In two ways. First, just as the sheaf of grain that was waved before the Lord was the first fruits that pointed to a fuller harvest down the road, so we also see in 1 Cor. 15:20 that Christ is the first fruits of those who have fallen asleep. In other words, Jesus was the first to be raised from the dead, but as a promise of a fuller harvest down the road when other believers would be resurrected from the dead.
Secondly, the New Testament term for the Feast of Harvest was Pentecost. Pentecost comes from the Greek Word for fifty. Well what had happened almost fifty days before Pentecost? Jesus Christ and his disciples were celebrating the Passover and the next day Jesus would shed his blood as the Passover or Sacrificial Lamb. He would later be raised as the first fruits of those who had fallen asleep.
Now fast forward fifty days, and the Jews are gathering in Jerusalem to cap off the Feast of Harvest, to celebrate the first full harvest of the year. And God sends down the Holy Spirit and 3,000 people trust in Jesus on that day. In other words, the Feast of Harvest was pointing to God's great harvest of souls. Just as the Feast of Harvest celebrated the first harvest of the year, the great spiritual harvest of Christians began at Pentecost with God saving 3,000 men and women by the power of His Spirit.