Lag B'Omer is a minor festival which is observed, as its name suggests, on the 33rd day of the seven week counting of the Omer between Pesach and Shavuot. Its Hebrew calendar date is the 18th of Iyar, which this year, falls out on the 11th of May.
In the times of the Temples in Jerusalem, an omer (a specific measure) of barley was offered by all farmers in Israel on the second day of Pesach. Until that offering was made, no breads or grains were allowed to be consumed (Leviticus 23:14). From that day onwards, the farmers would count forty-nine days till Shavuot, the festival of the wheat harvest, when they would make the pilgrimage again to Jerusalem.
The reason for the semi-mourning (no weddings or celebrations or haircuts) observed during the period of the Omer is found in the Talmud (Yevamot 62b) which describes how a plague killed the 24,000 students of Rabbi Akiva (1CE). The plague ceased on Lag B'Omer.
During the period of the Omer, 350 years ago, the Chmielnicki massacres took place in Russia, and thousands of Jewish men, women and children were killed.
On Lag B'Omer, the Jewish rebel Bar Kochba secured a victory against the Romans after a series of defeats.
There is a tradition that suggests that in the time of the Jews wandering the desert, the manna began to fall from heaven on this date.
Rabbi Shimon Bar Yochai (author of the Zohar, celebrated in particular by the Kabbalists) died on Lag B'Omer. Kabbalists and Hasidim gather at his grave in Meron (in the Galilee, Israel) on Lag B'Omer, lighting bonfires, giving their young sons their first haircuts, and dancing and singing throughout the night.
Bonfires are the main way this day is celebrated in Israel and the Diaspora, amongst both religious and secular Jews. Fire represents the conversion of material into energy - similar to a central Kabbalistic concept of "releasing sparks of holiness" (spiritual potential) inherent in the material world.