God commanded Israel to keep the feasts of Passover, Unleavened Bread, Firstfruits, Pentecost, Feast of Trumpets, Day of Atonement, feast of booths, which were types and shadows of what Jesus would do. The seven feasts consisted of three periods: The first period consisted of Passover and Unleavened Bread; the second period consisted of the Feast of Firstfruits and the Feast of Seventy Days (Pentecost); and the third period consisted of the Feast of Trumpets, the Day of Atonement, and the Feast of Tabernacles.

Passover commemorates the deliverance from Egypt, Unleavened Bread commemorates Israel's suffering, Firstfruits commemorates the crossing of the Red Sea, and Pentecost commemorates the ascent of the mountain to receive the first Ten Commandments. The Feast of Trumpets commemorates the blowing of the trumpet of repentance, the Day of Atonement commemorates the receiving of the second Ten Commandments, and Sukkot commemorates the gathering of materials for the building of the Temple.

All of these feasts were observed in the temple, and each had its own way of being celebrated. Passover was celebrated by killing a year-old male lamb and eating its meat, and the Feast of Unleavened Bread was celebrated by eating unleavened bread and bitter herbs for seven days. The Feast of Firstfruits was observed by offering to God the first ripe fruit of the grain; the Feast of Weeks was observed by offering to God the sheaves of the harvest; the Feast of Trumpets was observed by proclaiming repentance with a long blast of the trumpet; and the Day of Atonement was when the high priest entered the holy of holies and handed over all the sins to Azazel to cleanse the temple. And they hewed down a tree from the mountain, and made a tabernacle of it, and dwelt in it, and kept the feast of tabernacles: and this was the ordinance of the feast.

But these feasts were types and shadows of what Jesus would accomplish. Jesus fulfilled the prophecy through seven feasts in three stages, in the following order.

1) First Feasts (Passover and Unleavened Bread)

Jesus was sacrificed on the cross as the Passover lamb, freeing spiritual Israel from the sins represented by Egypt, and then laid in the tomb. The disciples were afraid and anxious, and this was the fulfillment of the prophecies of Passover and Unleavened Bread. Jesus' death as the Passover lamb is the fulfillment of Passover, and his lying in the tomb is the fulfillment of Unleavened Bread.

2) Second Period Feasts (Feast of Firstfruits and Seventy Days)

Jesus fulfilled the prophecy of the Feast of Firstfruits by rising from the dead as the firstfruits. (1 Corinthians 15:20) He also fulfilled the prophecy of the Pentecost by raising the dead in their graves and taking them to heaven after his resurrection. (Matthew 27:50-53)

3) Third Feast of Weeks (Feast of Trumpets, Day of Atonement, feast of booths)

The resurrected Jesus ascended into heaven on the 40th day. Before his ascension, he asked his disciples not to leave Jerusalem because he would give them the Holy Spirit in 10 days, so they gathered their hearts and purified themselves in prayer. The Holy Spirit is given to those who repent (Isaiah 59:20), and by saying this 10 days in advance, Jesus fulfilled the prophecy of the Feast of Trumpets, when the trumpets of repentance were blown Jesus' ascension fulfilled the prophecy of the high priest entering the Holy of Holies on the Day of Atonement, and Jesus' casting of Satan from heaven to earth fulfilled the prophecy of the Day of Atonement, when the high priest gives all sins to a goat and throws it into the wilderness (Revelation 12:7-9).

Jesus then came into the bodies of the saints by the Holy Spirit and wrote the word of God on their hearts. Just as Israel received the Word of God through the Ten Commandments, the saints received the new Word of God through the Holy Spirit, so the prophecy of the Day of Atonement was fulfilled when the Holy Spirit came upon the saints. The prophecy of the Feast of Tabernacles was also fulfilled because the saints who received the Holy Spirit became the temple of God where the Holy Spirit dwells.

Just as Israel, having completed the Day of Atonement, cut down trees from the mountain to build a tabernacle (sanctuary) and dwelt in it, so Jesus, in accordance with the prophecy of the Day of Atonement, cast out Satan from heaven, and by the Holy Spirit came into the bodies of the saints, inscribed the word of God (the Ten Commandments) on them, and made their bodies a temple in which He dwells, so that the prophecies of the Day of Atonement and the Feast of Tabernacles were fulfilled together (1 Corinthians 3:16)

Therefore, Jesus fulfilled all the prophecies about the feasts, so there is no need to offer sacrifices for sin again. 

[Hebrews 10:18] For sins and trespasses have been forgiven, and there is no longer any need for sacrifices to take away sins.