Pentecost is celebrated 50 days after the Passover. It is originally a Jewish Holy Day celebrating the first-fruits of the harvest and the revelation of the Law on the Mountain. There is a spiritual connection between those two which is revealed in the Christian celebration.
Jesus Christ is the first fruits of the Christian faith.
1 Corinthians 15:20 But now is Christ risen from the dead, and become the firstfruits of them that slept.
He was raised on the 1st day of the week and on the first day beginning the season of First Fruits which ends on the 50th day with Pentecost. Pentecost is known as the Feast of Harvests in the OT Scriptures.
It is also on this day that the Jews received the Law on the Mountain in the Sinai desert. And it is on this day that the Holy Spirit descended upon the Apostles in the upper room and they received the power to proclaim the Gospel throughout the world.
When the time for Pentecost was fulfilled,
they were all in one place together.
And suddenly there came from the sky
a noise like a strong driving wind,
and it filled the entire house in which they were.
Then there appeared to them tongues as of fire,
which parted and came to rest on each one of them.
And they were all filled with the Holy Spirit
and began to speak in different tongues,
as the Spirit enabled them to proclaim.
Pentecost is also regarded as the Birthday of the Church. The day that the Apostles were confirmed with the power to preach the Gospel to the world.
In the first book, Theophilus,
I dealt with all that Jesus did and taught
until the day he was taken up,
after giving instructions through the Holy Spirit
to the apostles whom he had chosen.
He presented himself alive to them
by many proofs after he had suffered,
appearing to them during forty days
and speaking about the kingdom of God.
While meeting with them,
he enjoined them not to depart from Jerusalem,
but to wait for “the promise of the Father
about which you have heard me speak;
for John baptized with water,
but in a few days you will be baptized with the Holy Spirit.”
When they had gathered together they asked him,
“Lord, are you at this time going to restore the kingdom to Israel?”
He answered them, “It is not for you to know the times or seasons
that the Father has established by his own authority.
But you will receive power when the Holy Spirit comes upon you,
and you will be my witnesses in Jerusalem,
throughout Judea and Samaria,
and to the ends of the earth.”