The term "Lag" is the abbreviation of the Hebrew letters lamed (L) and gimmel (G) whose numerical equivalents are 30 and 3 respectively. B'Omer means "the [counting] of the Omer."
Two significant events occurred on this date, and though separated by many years, they both contribute to its special status. On the thirty-third day of the counting of the Omer, the epidemic rampant among Rabbi Akiva's students abruptly ceased. Because the epidemic lasted 33 days, the common custom is to observe 33 days of mourning during the Omer period, ending on Lag B'Omer. It is also customary to mark the day with festive practices. The most colorful of these is a grand celebration of Mount Meron in Israel, at the grave of Rabbi Shimon bar (son of) Yochai.
The greatest scholar of the Kabbalah (Jewish mysticism) who ever lived, Rabbi Shimon died on Lag B'Omer, and on that day he revealed many of the deepest ideas of the Kabbalah to his students. They recorded his teachings in a book known as the Zohar, the Light. Ancient Jewish custom dictates that the anniversary of the death of a great scholar should be noted as a means of inspiring people with his lessons and teaching.
For hundreds of years on Lag B'Omer, people have gone to the grave of Rabbi Shimon on Mount Meron in the Galilee region. There they celebrated by lighting bonfires to symbolized the light of Torah that Rabbi Shimon revealed, and by dancing, singing and studying Rabbi Shimon's teachings. Today it is common to see people all over Israel celebrating Lag B'Omer with bonfires and singing, while at Mt. Meron itself, hundreds of thousands participate in the festivities.