Pentecost was the Greek name for the Jewish festival of Shavuot, which occurred fifty days after Passover and celebrated the beginning of the early wheat harvest. This meant that Pentecost always fell sometime during the middle of the month of May or occasionally in early June.
We celebrate Pentecost on the seventh Sunday after Easter, and so the Christian and Jewish celebrations do not always fall on the same day. Christians celebrate the coming of the Holy Spirit, as is told in the Book of Acts:
Jesus ordered them not to leave Jerusalem, but to wait there for the promise of the Father. “This,” he said, “is what you have heard from me; for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.” (Acts 1:4)
When the day of Pentecost had come, they were all together in one place. And suddenly from heaven there came a sound like the rush of a violent wind, and it filled the entire house where they were sitting. Divided tongues, as of fire, appeared among them, and a tongue rested on each of them. All of them were filled with the Holy Spirit and began to speak in other languages, as the Spirit gave them ability. (Acts 2:1-4)