Shavuoth – The Feast of Weeks
The fifty days between Passover (the Barley harvest) and Shavuoth (the Feast of Weeks, also the Wheat Harvest) are counted by the "omer" -- a sheaf of wheat brought to the Temple as a grain offering after Passover. This is a period of solemnity because of a plague during the time of Rabbi Akiva (around 130 CE). There was one day during the time of Akiva when there was a respite from the plague, and that is the Lag B’omer (the 33rd day of counting the Omer), which is now a day of rejoicing.
Shavuoth became associated with the receipt of the Torah at Sinai by the rabbis. There's no reference to this in the Torah, but it is now part of our tradition, celebrated by studying Torah all night. There are no traditional Shavuoth foods per se, although it is customary to have a dairy meal. This, we are told, was because once we had the laws of Kosher in the Torah, our ancestors could not eat the meat they had because it was non-Kosher, so they must have eaten dairy meals until they could prepare and eat an appropriate animal.
Shavuoth is one of the three Pilgrimage Holidays (Passover and Sukkoth are the other two).