The "Birthday of the Church"
(Ancient Greek: "the fiftieth [day]") is the Greek name for Shavuot, the Feast of Weeks, a prominent feast in the calendar of ancient Israel celebrating the giving of the Law on Sinai. This feast is still celebrated in Judaism as Shavuot. Later, in the Christian liturgical year, it became a feast commemorating the descent of the Holy Spirit upon the Apostles and other followers of Jesus Christ (120 in all), as described in the Acts of the Apostles 2:1–31. For this reason, Pentecost is sometimes described by some Christians today as the "Birthday of the Church".
Pentecost is celebrated fifty days after Easter Sunday, hence its name. Pentecost falls on the tenth day after Ascension Thursday (which falls 40 days after Easter). The season of Pentecost continues until the last Sunday of the church year, Christ the King Sunday, the Sunday before the First Sunday of Advent.
This information is pulled from http://en.wikipedia.org/wiki/Pentecost