As one of the most important solemnities on the Church's calendar, it has a rich depth of meaning, but here is how Pope Benedict summarized it in 2012:
This Solemnity makes us remember and relive the outpouring of the Holy Spirit on the Apostles and the other disciples gathered in prayer with the Virgin Mary in the Upper Room (cf. Acts 2:1-11). Jesus, risen and ascended into Heaven, sent his Spirit to the Church so that every Christian might participate in his own divine life and become his valid witness in the world. The Holy Spirit, breaking into history, defeats aridity, opens hearts to hope, stimulates and fosters in us an interior maturity in our relationship with God and with our neighbor.
To read the entire article, 8 things to know and share about Pentecost, please go to Jimmy Akin's article at National Catholic Register