Whitsunday is another name for the feast day of Pentecost, celebrating when the Holy Spirit came to the disciples of Jesus and granted them tongues of fire, blessing them with the strength to spread the word of God. I’m having a hard time finding when and where this phrase would be commonly used over Pentecost. I came across the term in Lawrence Block’s compelling mystery novel, The Sins of the Father.
Whitsunday is obviously a shortening of White Sunday. The O.A.D. suggests that the name comes from the white robes of the newly baptized. The O.E.D. points out that the whole week following the holiday was known as Whitweek, with Whitmonday, Whittuesday, and so on and so forth.