The OT Torah specified three priority festivals each year: Passover, Sukkot, and Shavuot; per Ex 23:14, on each of these holy days the Israelites were to keep a feast. Passover is very familiar to Christians as the Feast of Unleavened Bread and exactly corresponds to our own Easter (which we actually call Passover in the Latin and Greek languages); the Last Supper was a Passover Seder. Sukkot, or the Feast of Tabernacles, is known to Christians by references in the NT (see here). Shavuot, or the Feast of Weeks, is perhaps the least known to Christians of these three festivals as it is not mentioned in the Gospels, but we should become acquainted with it; Greek speaking Jews called it Pentecost, and it exactly corresponds to the Christian holy day of the same name. Let's look at the explanation of this Jewish holy day in the OT.
15 And you shall count from the morrow after the sabbath, from the day that you brought the sheaf of the wave offering; seven full weeks shall they be, 16 counting fifty days to the morrow after the seventh sabbath; then you shall present a cereal offering of new grain to the LORD. 17 You shall bring from your dwellings two loaves of bread to be waved, made of two tenths of an ephah; they shall be of fine flour, they shall be baked with leaven, as first fruits to the LORD. 18 And you shall present with the bread seven lambs a year old without blemish, and one young bull, and two rams; they shall be a burnt offering to the LORD, with their cereal offering and their drink offerings, an offering by fire, a pleasing odor to the LORD. 19 And you shall offer one male goat for a sin offering, and two male lambs a year old as a sacrifice of peace offerings. 20 And the priest shall wave them with the bread of the first fruits as a wave offering before the LORD, with the two lambs; they shall be holy to the LORD for the priest. 21 And you shall make proclamation on the same day; you shall hold a holy convocation; you shall do no laborious work: it is a statute for ever in all your dwellings throughout your generations. 22"And when you reap the harvest of your land, you shall not reap your field to its very border, nor shall you gather the gleanings after your harvest; you shall leave them for the poor and for the stranger: I am the LORD your God. (Lev 23:15-22)
Pentecost was a harvest festival of wheat and began on the 50th day after Passover – seven weeks being in between. We see here our covenantal number seven in the seven weeks, seven Sabbaths, and seven lambs. We also see our Eucharistic imagery in the wheat, the offerings (especially the peace offering) and the lambs. But there is one more element: the gleanings of the harvest were to be left for the poor – as applied to our Eucharistic image, we bring Jesus out to others as missionaries.
But there is another aspect to this Feast of Weeks that is found in Talmud, that is, the ancient traditions of the rabbis. They taught that 50 days after that first Passover, when the Israelites left their bondage in Egypt, God gave the Law to Moses on Mt. Sinai. This second meaning is embedded into this feast even to this day. The Bible does not specify that there were exactly 50 days from Passover to Sinai; but what it does say on this timetable was interpreted by the ancient rabbis as such. This is what the Jews of Jesus’ day believed. Shavuot/Pentecost has, then, two commemorative elements: (1) the wheat harvest, and (2) the giving of the Law.
We Christians also have a holy day called Pentecost. It is the well-known narrative of Acts 2:1-42, when the Holy Spirit descended onto the Apostles:
1 When the day of Pentecost had come, they were all together in one place. 2 And suddenly a sound came from heaven like the rush of a mighty wind, and it filled all the house where they were sitting. 3 And there appeared to them tongues as of fire, distributed and resting on each one of them. 4 And they were all filled with the Holy Spirit and began to speak in other tongues, as the Spirit gave them utterance. (Acts 2:1-4)
This also occurred 50 days after Easter, our Christian Passover. We can notice two things here. First, as the Jewish Pentecost commemorated the descent of the Lord on to Mt. Sinai fifty days after that first Passover, so we commemorate the descent of the Holy Spirit fifty days after our Passover. As God came to Moses on Mt. Sinai with fire and storm (Ex 19:16-20), so the Holy Spirit came to the Apostles with a mighty wind and tongues of fire. And, as God gave the Law to Moses on that 50th day, so the Holy Spirit gave the new law of grace to the Apostles on that 50th day.
5 Now there were dwelling in Jerusalem Jews, devout men from every nation under heaven. 6 And at this sound the multitude came together, and they were bewildered, because each one heard them speaking in his own language. 7 And they were amazed and wondered, saying, "Are not all these who are speaking Galileans? 8 And how is it that we hear, each of us in his own native language? 9 Par'thians and Medes and E'lamites and residents of Mesopota'mia, Judea and Cappado'cia, Pontus and Asia, 10 Phryg'ia and Pamphyl'ia, Egypt and the parts of Libya belonging to Cyre'ne, and visitors from Rome, both Jews and proselytes,11 Cretans and Arabians, we hear them telling in our own tongues the mighty works of God. (Acts 2:5-11)
Second, as we noted above, the Jewish Feast of Weeks was one of three special holydays; at the time of the Apostles, all Jewish men were required to make a pilgrimage to Jerusalem on each of these feasts every year. The reason there “were dwelling in Jerusalem Jews, devout men from every nation under heaven” is that they were there fulfilling their obligation for the Feast of Weeks pilgrimage. As the first Easter coincided with the Jewish Passover, so 50 days later our Christian Pentecost coincided with the Jewish Pentecost. This is the meaning of Acts 2:1 mentioning “the day of Pentecost.”
What was the result of that first Pentecost? It was that the Apostles, those first priests, received a power of the Holy Spirit enabling them to bear witness to Christ. They preached miraculously, such that every Jew could understand their preaching regardless of language (the undoing of the Tower of Babel). And they believed.
41 So those who received his word were baptized, and there were added that day about three thousand souls. 42 And they devoted themselves to the apostles' teaching and fellowship, to the breaking of bread and the prayers. (Acts 2:41-42)
The result was 3,000 new believers! Just as the Jewish Pentecost demanded the gleanings of wheat be given to the poor, to those who had no wheat, so the Christian Pentecost brought Jesus to the non-believers. And it was the Eucharistic Jesus they received, for “they devoted themselves… to the breaking of bread and the prayers.” The Jewish harvest feast became a harvest of souls.
(Interesting observation: Contrast this new life given to 3,000 souls on Pentecost with the old Pentecost, when God gave the law to Moses; read Ex 32:28 – 3,000 unfaithful souls died, executed for worshipping the golden calf. What was lost in the old, God restored in the new.)
Our Christian Pentecost is, then, the fulfillment of the OT Pentecost of Lev 23. The OT Feast of Weeks is a type of the missionary aspect of our Eucharist. Not only are there Eucharistic elements in the OT feast, but a directive to share the wheat with those who have none. We commemorate Pentecost every year as one of our own three special holy days (Easter, Pentecost, Christmas); it is our Feast of the Holy Spirit, commemorating His powerful gifts that we receive and use to evangelize, to harvest souls.