The Catechism in Questions & Answers

712. What is the significance of Pentecost?

On Pentecost—fifty days after Jesus’ resurrection—we commemorate the day on which the Holy Spirit was poured out. We also speak of Pentecost as the “birthday of the church of Christ”. After the outpouring of the Holy Spirit, Apostle Peter delivered a powerful sermon which centred on the crucified and resurrected Christ, who had ascended into heaven.
Moreover, Pentecost is a celebration of joy over the fact that the Holy Spirit is present and active in the church.

Pentecost: see Questions 209., 422., 520., 582.