Fifty days are counted between Passover and Shavuot. Those days, which should have been days of joy and preparation for the receiving of the Torah, turned out to be days of semi-mourning. No weddings are allowed, no music and no hair-cuts. This count is called Sefirat Ha'Omer. And yet, on the 33 day of this count, the 18th day of the Hebrew month Iyar, Lag Ba'Omer is celebrated. Indeed, this is the most mysterious holiday in the Jewish tradition?
By 135 CE, 65 years after the destruction of the 2nd temple, the Roman Empire was corrupt and falling apart. At that time, a man named Shimon Bar Kochva organized an army to fight against the Romans. He managed to organize a big and strong army, and also had the support of the religious leaders in Judea, especially that of Rabbi Akiva and his followers. Bar Kochva and his army were very successful, and managed to establish an independent country for almost five years before they were defeated by the Romans. Rabbi Akiva and many others thought that Bar Kochva was the Messiah, which is understandable considering this unexpected military success.
However, pretty soon the downfall of Bar Kochva began: First of all, he accused a man named Rabbi Elazar of betrayal and murdered him. Immediately he lost the support of Rabbi Akiva, and instead of calling him Bar Kochva (which means "son of a star") he started calling him Bar Koziva ("son of a lie"), for he realized that Bar Kochva was not the real Messiah. At the same time, there was an outburst of plague, which killed many of his soldiers (among them the 24000 followers of Rabbi Akiva).
How does all this relate to Lag Ba'Omer and Sefirat Ha'Omer?
Some believe that the plague was a punishment as a result of the lack of respect among the 24000 soldiers who were Rabbi Akiva's students. The Mourning between Passover and Shavuot is in memory of the soldiers who died in the plague. A second reason for this mourning is the failure to bring the Messianic Age, and the downfall of the almost independent country that was established. With the death of those soldiers, the messianic hope died too for many years.
One speculation is that on the 33rd day of the Omer that year, the plague stopped. Another theory is that on that date Jerusalem was reconquered by Bar Kochva and his army. Others believe that this was the date on which the rebellion began. A forth reason for the celebration is to commemorate Rabbi Shimon Bar Yochai, who lived at that time and wrote the book of the Zohar, which is the basis for the Kabbalah.