The Feast of Weeks, also known as Harvest (Exodus 23:16), Shavuot (Hebrew), or Pentecost, was a festival of joy and thanksgiving celebrating the completion of the wheat harvest. All of the feasts given by Yahweh were related to the harvest, which is a metaphor for His plan of redemption (see Harvests Of Redemption. It was the second major feast in which all able-bodied Jewish males were required to celebrate in Jerusalem (the other two being Passover and the Feast of Tabernacles). It was celebrated as a sabbath with rest from ordinary labors and the calling of a holy convocation (Leviticus 23:21; Numbers 28:26).
It is called the Feast of Weeks because God specifically told His people that they were to count seven sabbaths complete (seven complete weeks plus any new moon days) from Firstfruits (Leviticus 23:15; Deuteronomy 16:9), and then on the "morrow" 50 more days, then this fourth feast was to be observed (Luke 23:16). This fourth feast was to occur 7 weeks plus fifty days after Firstfruits (Christ's resurrection). Therefore, the feast was given the name "Pentecost" (Acts 2:1) which means "fifty."
On this occasion, the children of Israel were not to simply bring the firstfruits of the wheat to the Temple (as they brought the firstfruit of the barley at the Feast of Firstfruits), but rather two loaves of bread. These two loaves were specifically commanded to be made with fine flour and baked with leaven (Leviticus 23:17), and they were to be used as a "wave offering" for the people. The leaven indicates the presence of sin. Yahweh's people of the wheat harvest are not yet perfected.
Passover signifies Yahushua (the Messiah's) victory over Satan and sin at His death. He was raised on the Day of First-Fruits. Jesus (Yahushua, the Messiah) was the First of the First-Fruits, the First of the Barley Harvest.
The Feast of Weeks symbolically pointed to the coming of the Holy Spirit and the beginning of the Kingdom. The Son of God arose from the grave on Firstfruits. He then spent forty days with His disciples in post-resurrection ministry (Acts 1:3).
Immediately after forty days, Jesus informed them that it was necessary that He leave them and ascend to His Father in Heaven (in order to apply the benefits of His once and for all sacrifice). However, He told His disciples that they would not be left abandoned and comfortless. He would then send them His Holy Spirit who would come alongside to help in His absence (John 14:16-17).
More importantly, and on a grander scale, this feast points to the final Wheat Harvest when the wheat is separated from the chaff and Yahweh's people represented by the wheat are purified and redeemed.