Lag Ba'Omer is one of the most obscure and mysterious dates on the Jewish calendar. Many events and characters are connected with it: the death of R' Akiva's disciples, the day of R' Shim'on Bar Yochai's passing – and the celebrations connected with it, the Bar Kochva revolt, the custom of lighting bonfires, and more.
The Death of R' Akiva's Disciples
The Talmud (Tractate Yevamot 62B) recounts that the pupils died between Pesach and Atzeret (Shavu'ot), because they did not treat each other with respect. The Talmud does not, however, mention the date of Lag Ba'Omer itself, and we first hear of it only during the period of the Rishonim. R' Zerachia Ha'Levy opines that the correct version in the Talmud is "they all died from Pesach until the approach of Atzeret ", which means half a month before Shavuot, thus bringing us to Lag Ba'Omer. The Me'iri says that Gaonic tradition is that the death of the pupils ceased on Lag Ba'Omer.
Therefore, the Shulchan Aruch rules that the mourning customs of Sefirat Ha'omer prevail only until Lag Ba'Omer. The Rema (R' Moshe Isserles) adds that on Lag Ba'Omer itself we do not practice mourning, and "…we rejoice more than usual (on this day) and do not say Tachanun".
Why Do We Rejoice on Lag Ba'Omer?
The Pri Chadash (R' Hezekiah da Silva) raises a tremendous question concerning the joyous customs on Lag Ba'Omer:
"However we must understand precisely the reason for this rejoicing. If it is because they ceased to die – what of it? Not one of them was left, and surely this is no cause for joy?!"
The reason the deaths ceased was not, according to the Talmud, that the cause of the diphtheria epidemic (the lack of mutual respect among thedisciples) had been rectified. The epidemic ceased because no disciples were left "and the world was barren, desolate". So why rejoice on Lag Ba'Omer?
The Pri Chadash replies briefly that the joy is "due to the additional pupils R' Akiva acquired afterwards, who did not die". In order to appreciate the depth of this answer, let us study the continuation of the Talmudic passage:
"They said: R' Akiva had twelve thousand pairs of disciples, from G'vat to Antipares, and they all died during the same period of time, because they did not treat each other respectfully. And the world was barren (of Torah), until R' Akiva went to the Sages in the south and taught them: R' Meir, R' Yehuda, R' Yossi, R' Shim'on' and R' Elazar ben Shamua, and they re-established the Torah at that time."
After the death of R' Akiva's pupils the world was barren of Torah. The situation was so perilous as to cause the Sages to dread that "Torah will be forgotten from Am Yisrael" (see Tractate Shabbat p.138B). R' Akiva was the greatest of his generation, and after his disciples' death the fear that the Torah would, G-d forbid, be forgotten in the future was very real.
However, in the end R' Akiva found the way to renew the world of Torah, by going south and teaching the Rabbis there his method of learning, and "they re-established Torah". Indeed, the Talmud in Sanhedrin (86A) says:
"Unless otherwise specified, a Mishna is according to R' Meir, a Tosefta is according to R' Nechemia, a Sifra is according to R' Yehuda, a Sifre – according to R' Shim'on, and all these are based on R' Akiva's teachings."
In other words, most of Oral Law (Torah SheBe'al Peh) – the Mishna, the Tosefta and the Halachic Midrashim - derive from R' Akiva, by way of these five new disciples!
And so it seems that the reason for our great joy on Lag Ba'Omer is the revival of the Torah world. After the epidemic that killed R' Akiva's pupils and left the world of Torah bereft, came a period of rehabilitation – during which R' Akiva taught his new pupils who "re-established Torah in Israel". In the Sdei Chemed's words:
"When the day of Lag Ba'Omer arrived – R' Akiva ordained his five great disciples, who did not die, and who taught Torah in public".
On Lag Ba'Omer we joyfully celebrate the renewal of the Oral Law. On this day we received the power to continue learning and sustaining the Oral Law, passed on to us by R' Akiva. On this day it became clear that even though almost all the great scholars died – the Torah itself is eternal, and will exist forever in Am Yisrael. It will find the way - in each and every generation - to lead our People on!
 Brought in Sefer Ha'Manhig by R' Avraham ben Natan, .אירוסין עמ' תקל"ח
According to the Talmud in Bechorot p. 58A.
On Yevamot ibid. s.v. .אע"פ
 .תצ"ג, א-ב
 Ibid. .ב'
 Part 4, .אסיפת דינים, מערכת ארץ ישראל, אות ו', ד"ה ומ"ש השו"מ