In Judaism, Pentecost is also called (Hag) Shavuot, and was the 50th day after the Passover offering of a sheaf of wheat. Pentecost was originally a harvest festival that came to be associated with Moses' law-giving at Mt. Sinai.
In Christianity, Pentecost is also called Whitsunday, and is the 50th day after Easter. Pentecost came to be the favored time for baptisms when the newly baptized wore white, for which reason the holiday is called White Sunday or Whitsunday. Pentecost is held to be the birthday of the Christian Church.
For more on the Jewish version of Pentecost, see Shavuot, from Lisa Katz, About.com Guide to Judaism.
For more on the Christian version of Pentecost, see Pentecost 101, from Scott P. Richert, About.com Guide to Catholicism.
Shavuot is celebrated on 6 Sivan worldwide and also on 7 Sivan outside Israel. Source: About.com Guide to Geography