At this point in the New Testament, Jesus is said to have already ascended to Heaven (which the aptly named Ascension Day celebrated this past Thursday). According to the Acts of the Apostles, he promised that he wouldn't abandon his followers — he'd send the Holy Spirit down to them not long after his departure. And, when that time came, the Holy Spirit is said to have arrived in a gust of wind and fire, giving the apostles the ability to speak many languages so they could spread the word of God to as many people as possible.
Interestingly, Pentecost has ties to another religion: Just as the Jewish holiday Shavuot occurs 50 days after Passover, Pentecost falls on the 50th day after Easter. These two celebrations share roots in the Feast of Weeks, a Jewish harvest festival which took place seven weeks (or roughly 50 days) after Passover. Beyond that, they both commemorate highly significant events in their respective religions (where Pentecost celebrates the arrival of the Holy Spirit, Shavuot celebrates God giving the Torah to the Israelites).
Today, Pentecost is still a meaningful day for baptism within Eastern and Western forms of Christianity. It's actually known as Whit Sunday in many European countries because of the white robes that people will wear when they're baptized.
Masses held for Pentecost usually feature readings from the Acts of the Apostles and, in a nod to the Holy Spirit imbuing the apostles with languages (or "fiery tongues"), some churches will be decorated with red rose petals and officiants will wear red robes.
Pentecost is a chance for Christians to reflect on how they feel the Holy Spirit's presence in their own lives. Though it may not be the most prominent Christian holiday, it serves as a powerful reminder that, regardless of their language or where they come from, all Christians are united in their faith, particularly in their worship of the Holy Spirit.