The Jewish holiday of Shavuos begins Thursday evening, June 1.   There are a number of places in the Torah where we are commanded to celebrate this holiday. Including:

Deuteronomy 16:9 You shall count seven weeks for yourself; from[the time] the sickle is first put to the standing crop, you shall begin to count seven weeks.
10 And you shall perform the Festival of Weeks to the Lord, your God, the donation you can afford to give, according to how the Lord, your God, shall bless you.
11 And you shall rejoice before the Lord, your God, -you, and your son, and your daughter, and your manservant, and your maidservant, and the Levite who is within your cities, and the stranger, and the orphan, and the widow, who are among you, in the place which the Lord, your God, will choose to establish His Name therein.

12 And you shall remember that you were a slave in Egypt, and you shall keep and perform these statutes.


Shavuot is the culmination of the counting of the 49 days of the Omer. These are the number of days between Passover and Shavuos.  It marks the giving of the Torah on Mt. Sinai. The Ten Commandments are read in synagogues on Shavuot just as they were in the desert on Mt. Sinai over 3,300 years ago.


More at the usual sites:

Chabad
Aish.com
Judaism 101
Jewish Virtual Library
OU.org


Note of interest - since Shavuot occurs 50 days after Passover, Christians gave it the name Pentecost. However, the actual Christian commemoration of Pentecost occurs on the seventh Sunday after Easter.