Pentecost begins 50 days after Easter Sunday. This liturgical season celebrates the descent of the Holy Spirit upon the Church and apostles. ( Acts 2:1-41)
The Vigil of Pentecost, like the Vigil of Easter, used to be a day for baptism. It had an almost similar liturgy as the Easter Vigil. The newly batised were clothed i white garments and therof comes the name Whitsunday.
Like the Church celebrates the Octave for Christmas and Easter, it also used to celebrate the Pentecost Octave in similar manner. In Norway we have a remainder of this on the Second Day of Pentecost (Whitmonday)