Lag BaOmer is in Hebrew known as the 33rd day of the Omer (Lag, is the gematria of 33). Lag BaOmer falls on the 33rd day of the counting of the Omer, as counted from the second day of Pesach until the holiday of Shavuot. This corresponds to the 18th day of the Hebrew month of Iyar.
The Talmud mentions that during the time of Rabbi Akiva, 24,000 of his students died from a divine-sent plague during the counting of the Omer. The Talmud relates this was because they did not show respect to one another, befitting their level; they were against each other, and each thought they were better than the other (Yevamot 62b). Jews celebrate Lag BaOmer, the 33rd day of the count, as the traditional day that this plague ended.
After the passing of Rabbi Akiva's 24,000 students, he educated only five students, among them was Rabbi Shimon bar Yochai. Rav Shimon went on to become the greatest teacher of Torah in his generation. The day of Lag BaOmer is celebrated as the Hillula or yahrzeit (anniversary of death) of Rav Shimon bar Yochai, who is purported to have written the Zohar, a landmark text of Jewish mysticism. According to our knowledge, on the day of Rav Shimon Bar Yochai's passing, he revealed the deepest secrets of the Kabbalah. Indeed this day is seen as a celebration of the handing over of the hidden, mystical Torah through Rabbi Shimon Bar Yochai, as a parallel to Shavuot, which celebrates the giving of the revealed Torah through Moses.
These five students that Rabbi Akiva taught became so great, much commentaries and teachings come from them. Much of the Oral Torah is from these great Rabbi's that we learn today!
As we don’t mourn on this day of the 33rd day of the Omer, weddings, parties, listening to music, and haircuts are commonly scheduled to coincide with this day. Families go on outings.
It is a custom to go to a place in Israel named Meron, the place where Rav Shimon Bar Yochai was buried, where celebrations, dating from the time of Rabbi Isaac Luria, that three-year-old boys are given their first haircuts (upsherin), while their parents distribute wine and sweets. Similar celebrations are simultaneously held in Jerusalem at the grave of Shimon Hatzaddik.
This is a festival where we honor Torah scholars, and show the great Torah teachers respect. A Torah teacher can teach his students and help them enter the world to come. One should give a Torah scholar respect and for example stand up for them when entering a room.
In the Tanach in the book of Shoftim, we learn how Othniel Ben Anaz became the leader of the Jewish people as he studied and re introduced many different Jewish laws that were forgotten from the time of Mount Sinai (Temura 15/16).
According to the Chatam Sofer, another occurrence in Biblical history on the day of Lag BaOmer is, if we cast our minds back to Parshat Beshalach, the day that the Heavenly Bread (Shemot 16:4/21) started coming down for the Jews was on the exact day of Lag BaOmer, this was a spiritual food, that the Jews lived on for 40 years in the merit of the great Torah teacher, Moshe, in the wildnerness (Taanit 9).