Lag Baomer celebrates the yohrtzeit of a tzadik. Why is that cause for celebration?
Certainly for those of a Hassidic or Kabbalistic bent, observing Lag BaOmer tied to R' Shimon Bar Yochai's death is a big deal.
For a more critical (Mitnagdic?) view, try this lecture from Rabbi Dr. Shnayer Leiman on the subject.
He, like the Chasam Sofer before him, reflect the non-Hassidic view of being unsure about where the whole thing came from.
One possibility suggested is it was originally "Yom Simchas Rashbi", the day of Rabbi Shimon bar Yochai's rejoicing; and some typo changed it to "Yom Shemes Rashbi", the day of his death.
The Simcha of Lag Baomer is a strange concept. The Shulchan Aruch says that on the day a Tzaddik dies you make a fast. Where did this day of happiness come from? The GR"A says it was the day that the students of Rabbi Akiva stopped dying. However, the question still stands. Rabbi Shimon Bar Yochai died on this day, so what is the celebration about?
The answer brought by the Kadmonim is that Rabbi Shimon Bar Yochai himself said there should be a celebration on the day of his death. The Shach in Hilchos Aveilus also brings down a similar premise that if a father says not to act like an Avel the full 12 months we follow his command. This is because the whole Halacha of mourning is only in honor of the parent. Therefore, if he asks you not to act in a manner of mourning then of course you listen.
Now we must understand why did Rabbi Shimon say to celebrate his death when we know that when a Tzaddik dies it is like the destruction of the Beis Hamikdash? There is yet another problem with the Lag Baomer celebrations in that both the Shoel Umashiv and the Chasam Sofer in their Seforim wrote in very strong language that the Minhag of burning clothes (which is prevalent at the Kever of Rabbi Shimon Bar Yochai in Miron) is a problem of Baal Taschis (Destroying things without Purpose) and (even worse) Darchei Amori (Behaving as a Idol worshiper). In defense of current practice, there is a Mesorah that the Ohr Hachaim Hakodesh followed the Minhag of burning clothing.
The Aruch Hashulchan provides another reason for celebrating Lag Ba'omer: this was the day when Rabbi Shimon and his son where finally allowed to leave the cave in which they where hiding. A hint to this concept is that the Gemora which says the story of Rabbi Shimon leaving the cave is on Daf Lamed Gimmel (the thirty third page). The Mon also started falling on Lag Ba'omer. There is also a Zohar in Parshas Hazinu which says that Rabbi Shimon said over the secrets of the torah on Lag Ba'omer, and that he died that day. His students where afraid that he would die before he would teach them the secrets of the Torah, so they were overjoyed after they were taught. In his final conversation Rabbi Shimon said "This whole day is in my control. Now I have the right to say over all the secrets before I go to the next world, so that I not be embarrassed when I go up to Shmayim."
There are two thousand two hundred and twenty five teachings from Rabbi Shimon Bar Yochai in the Sifra, Bavli, and Yerushalmi. However, the secrets of the Torah (the SOD) he was only able to tell over the day he died.
In conclusion, what is the answer to all of the above questions? The reason that the day a Tzaddik dies is so sad that it is considered similar to the destruction of the Beis HaMikdash is because of the loss of Torah to the people in this world. The Tzaddik is going to Gan Eden, so the only people who lose out are the people he leaves behind in this world.
The day Reb Shimon died is fundamentally different because (as the Zohar says) the secrets of the Torah (the actual text of the Zohar) was able to be said and written on this day. Therefore, it is not a day of sadness and fasting but a day like Purim and Shavous - a day of receiving the Torah of Nistar (the hidden aspects of Torah) and therefore a day full of joy happiness and a celebration.
The significance of the Mon with regards to Lag BaOmer was (as the Mamar Chazal says) that the Torah was only given to those who ate the Mon.
Now, to the final question of why burn the clothes? When Rabbi Shimon bar Yochai and his son Rabbi Elozor left the cave everything Rabbi Elozor looked at got BURNT. After which Rabbi Shimon would look there and it would return it to the way it was. The reason everything was burnt up was since they where so separated from the frivolity of this world, they could not stand to look at worldly things. The burning of the clothes symbolized that we should aspire to be like Rabbi Shimon and try to separate ourselves from the Gashmius of this world and try to live on a higher spiritual level. However, burning clothing to teach a moral lesson would still seem to be forbidden. However, this too can now be answered.
The Gemara in Meseches Tomid states when the Kohanim had guard duty and they feel asleep on the job ,the Gemara says "Reshus Hayah Lisrof Es bigadav" (the chief guard had the right to burn a sleeping Kohen's garments). This is a source which allows burning clothing to teach another lesson. This, however, is only allowed if there is a lesson to be learned. This answers the question of the Chasam Sofer and the Shoel Umashiv.
There is also the question of what is the reason for the fires? The simple answer given is just as we know we light a small candle for a soul on a Yahrtzeit like the Chazal say "Ner Hashem Nishmas Adam" therefore for a great soul we light a large fire. There is another answer given that Reb Shimon was on such a level that with his Ohr Hatorah he was able to stop the Night from coming therefore we light fires to symbolize the light of his torah that is still here.
The "simcha" of R. Shimon bar Yochi on Lag b'Omer is that he began his studies with R. Akiva. After the plague of R. Akiva's students ended, R. Shimon bar Yochi was one of the 5 students who formed the new generation of students to continue learning under R. Akiva.
(This accords with the manuscripts which say not that "he died" on Lag b'Omer but that it was the day of his "simcha"). The Ben Ish Chai elaborates on this point.
Eliezer Brodt claims here that the death aspect of it is all based on a misprint: Rabi Shim'on bar Yochai wasn't dead. He was happy!
According to this essay by Rabbi Yossi Jacobson:
Before his passing, Rabbi Shimon instructed his disciples to observe his yahrzeit (the day of his death) as a time of joy and festivity
The sources for this:
See Zohar vol. 3 p. 287b; p. 291a. Pri Aitz Chaim Shaar Sefiras Haomer chapter 7; Shaar Hakavanos Sefiras Haomer Derush # 12. Mishnas Chassidim (by Rabbi Amnuel Chei Riki) Mesechte Iyar 1:6.