Lag Ba'Omer is a short way of saying "the 33rd day of counting of the Omer." The first word of the holiday's name, Lag, is simply a combination of two Hebrew letters, lamed (which stands for the number thirty) and gimmel (which stands for the number three). Thus thirty-three.
Remember that Hebrew is so old a language that it came into being before there were actual numerals to stand for numbers. Therefore letters were used instead. In fact the numbers that we use today are called Arabic Numbers and they were not invented until about 800 years ago in the 1200's. Before that we used Roman Numerals, which were also made up of letters.
The name of the holiday actually means the thirty-third day of the counting of the Omer. So what does counting the Omer mean?
It is unlikely that anyone knows how many days there are between New Year's Day and July 4th, or between Sukkot and Hanukka off the top of his head. But all religious Jews know that there are precisely fifty days between the second day of Passover and Shavuot. During the first forty-nine days of this period, known as the Omer, each day is counted aloud during the evening service. After reciting a special blessing, "Blessed are You, Lord our God ... who has commanded us to count the Omer," congregants say, "Today is the third day (or twentieth or fortieth) in the Omer." On the fiftieth day Shavuoth is celebrated.
In Hebrew, Omer means sheaves of a harvested crop. (A sheaf is a tied bundle of cut stalks.) When the Temple stood in Jerusalem, priests would offer there, on behalf of all of Israel, newly harvested barley (an Omer) on the second day of Passover. Their doing so signaled the beginning of Israel's harvest season, a period that lasted seven weeks (forty-nine days). In the Torah, Shavout, which celebrates the giving of the Ten Commandments to Moses on Mount Sinai also celebrates the harvest's end on the fiftieth day after Passover.
Although one would think of the harvest period as joyous, in Jewish life the Omer is considered a time of semi-mourning. To this day, no scholar is sure why this is so. The Talmud speaks obscurely of a plague occurring on one Omer that killed 24,000 students of the second-century Rabbi Akiva. What kind of a plague was it that apparently only affected Rabbi Akiva's talmudic students and nobody else and came to an end on Lag Ba'Omer (the thirty-third of the forty-nine days)? Most modern scholars assume that the plague referred to was not an illness.
Rabbi Akiva supported a rebellion against the Roman conquerors of Israel led by a famous Jewish military leader by the name of Bar-Kochba. Moreover, Akiva declared Bar-Kochba to be the Messiah who would liberate the Jews from Roman domination. Although Bar-Kochba did achieve some early military successes, eventually the Romans suppressed his revolt with incredible brutality. Among Bar-Kochba's leading soldiers were thousands of Rabbi Akiva's students. Thus, it is likely that Lag Ba'Omer was a day on which the Jews either achieved a short lived victory over the Romans or gained some respite from the slaughter of battle.
So, the thirty-third day of the Omer, Lag Ba'Omer, is an exception to the semi-mourning. That day is a time of happy celebration, a day for weddings, picnics, and playfulness. It is observed by playing with toy bows and arrows, and celebrating around a bonfire with singing and dancing. Many Orthodox Jews give their three year old children their first haircut on Lag Ba'Omer and a party is held to celebrate the event. Lag Ba'Omer has always been a special day for school age children, so special that it was once the day when younger children could boss the older ones, who had to do as they were told. Lag Ba'Omer belongs to young people, it is your day.