Thanks for your question. I hope that I can do some justice to it as books have been written about the significance of the feasts under the Law of God as given to Moses. There were 7 feasts celebrated under the Law. If you count the Sabbath, there were 8 (see Leviticus 23:2,3).
The Feast of Passover - The significance of the Passover is deliverance from bondage by means of sacrifice. It was initially a deliverance of Israel from the bondage of Egypt. Its true significance is to be found in 1 Corinthians 5:7,8 "Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us: Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth." Jesus is the true Passover lamb of which those sacrificed at the Passover feasts of Israel were but the shadow. Christ is the substance and the reality of the Passover because through his sacrifice we are freed from the bondage of sin and death. Romans 8:2,3
The Feast of Unleavened Bread - Celebrated from the 15th to the 21st days of the month Abib. This feast immediately followed the Passover. It was a memorial to Israel of their deliverance from Egypt. The bread was unleavened because, at the beginning of the Exodus, they didn't have time to tarry while leaven caused the bread to rise. They had to eat their bread in haste because God was setting them free. It was a feast of joy in spite of the flat taste of the bread itself. Leaven belonged to Egypt. Unleavend bread belonged to their new life of freedom. The significance of this feast is clear in the New Testament. Leaven promotes fermentation and corruption. It is used in Scripture as a symbol of the corrupting effect of sin in the flesh. 1 Corinthians 5:6,7. The feast of unleavened bread is a continuation of the Passover and indicates the progression of the believer in his or her life in Christ. After joining with the sacrifice of Christ, our Passover, through the symbolic death and resurrection of baptism, the believer enters into a life free from sin (not that we don't sin but now we may be forgiven). This is the meaning of the 7-day period of unleavened bread. The 7 days symbolize a complete life. The believer abstains from sin (symbolized by the leaven). The spiritual significance of both the Passover feast and the Feast of Unleavened Bread are essential to the follower of Christ. His sacrifice is of no use to us unless the leaven of sin and corruption is continually purged from our lives. Likewise the purging of the leaven of sin and corruption is of no use unless it is sanctified by the Lord's atoning sacrifice - our Passover lamb. The feast of unleavened bread combined with the Passover illustrate brilliantly the two most fundamental aspects of our life in Christ.
The Feast of the Firstfruits - This feast immediately preceded the Feast of Pentecost (Feast of Weeks) See Leviticus 23:9-14; Deuteronomy 26:5-10. The "Firstfruits" foreshadowed the resurrection of Jesus and, by implication, our own. See 1 Corinthians 15:20-23 "But now is Christ risen from the dead, and become the firstfruits of them that slept. For since by man came death, by man came also the resurrection of the dead. For as in Adam all die, even so in Christ shall all be made alive. But every man in his own order: Christ the firstfruits; afterward they that are Christ's at his coming." It also symbolizes the need for every believer to give the first and the best of all his substance in the service of his Lord.
The Feast of Pentecost (or The Feast of Weeks) - After the Feast of the Firstfruits, the harvest could begin. The harvest was inaugurated by the Feast of Pentecost. It lasted for 7 weeks and ended with the harvest of wheat and rye. See Leviticus 23:15,16. It was closely related to the feast of Firstfruits as both had to do with the harvest. In this regard, we can see that it was necessary for the Lord, as the Firstfruits, to be offered before the great harvest attendant on the preaching of the Gospel to begin. That harvest would last for 7 weeks, symbolic of a perfect time period when God's purpose in ensuring that the whole world would hear the Gospel would be completed. We are now living in the time when the harvest will be complete because the "Times of the Gentiles" have been fulfilled. See Luke 21:24.
The Feast of Trumpets - about 4 months after the Feast of Pentecost which was kept on the 1st day of the 7th month. This was also the month of the Day of Atonement and the Feast of Tabernacles. The 7th month was regarded as a Sabbatical month. Rosh Hashanah was a special occasion regarded by the Jews as a day of judgement to be spent in prayer for mercy and forgiveness. There was a holy convocation or coming together on that day with a memorial blowing of trumpets. In Jerusalem, the trumpets were blown all day long. The trumpets were made of silver - a symbol of redemption. The silver was obtained from part of the atonement money paid in silver by each man as a "ransom" when they were numbered after the Exodus. See Exodus 30:12-16. The significance of this feast is in making known the Gospel message to those around us. In Old Testament times, the trumpets were blown by the priests whose duty it was to teach God's law to the people. In Christ, we have the same duty towards our friends and neighbours. See 1 Peter 2:9. This feast also forshadows the day when God will "blow the trumpet" and resurrection and judgement shall begin. See 1 Thessalonians 4:16 Psalm 89:15,16 "Blessed is the people that know the joyful (Hebrew = Trumpet) sound: they shall walk, O LORD, in the light of thy countenance. In thy name shall they rejoice all the day: and in thy righteousness shall they be exalted."
The Day of Atonement - In Hebrew, Yom Kippurim means the day of covering. It was not a feast day but rather a day of affliction, humbling and repentance. The ceremonial aspects of the Day of Atonement - Leviticus 16:29-34. It was designed to teach the principle that without the shedding of blood there is no forgiveness of sin - Hebrews 9:18-24. The word "Atonement" means a "covering" and in this case it signifies a covering for sin. The ultimate covering for the sin of the world was the sacrifice of the "Lamb of God." There are many other wonderful convergences with the activities under the Law connected with the Day of Atonement and with the work of the Lord Jesus and our relationship to it but time does not permit more than this overall consideration of its significance.
The Feast of Tabernacles - Considered to be the great feast of the Jewish year lasting 7 days and ending in a holy special sabbath. See Leviticus 23:39-44; Deuteronomy 16:14-17. The people were to gather together and live in booths (tents) to remind them of their wilderness wanderings. The significance of this feast will be fulfilled when, in the Kingdom age, the nations of the earth will come to Jerusalem to "keep the feast of tabernacles." Zechariah 14:16 cp. Isaiah 25:6-9 "And in this mountain shall the LORD of hosts make unto all people a feast of fat things, a feast of wines on the lees, of fat things full of marrow, of wines on the lees well refined. And he will destroy in this mountain the face of the covering cast over all people, and the vail that is spread over all nations. He will swallow up death in victory; and the Lord GOD will wipe away tears from off all faces; and the rebuke of his people shall he take away from off all the earth: for the LORD hath spoken it. And it shall be said in that day, Lo, this is our God; we have waited for him, and he will save us: this is the LORD; we have waited for him, we will be glad and rejoice in his salvation." Here is the meaning of the feast for the Millenial Kingdom and beyond. It is emphasised by the meaning of the plants used to construct the booths in which they dwelt. The palm for victory; the olive for peace and prosperity; the pine for beauty; the willow of the brook for security; and the myrtle in place of the prickly briar for happiness and comfort.
The Sabbath - This is of course the day of rest symbolizing in future the Kingdom of God and presently our rest or ceasing from sin as we enter into the saving work of Joshua (Jesus) who is leading us to the promised land of his Kingdom. For the believer, every day is a sabbath day.
I hope you find this helpful.
God bless and keep you,