The kohanim are commanded to avoid contact with corpses in order to maintain a high standard of ritual purity. They may attend the funeral of only their seven closest relatives: father, mother, wife, son, daughter, brother, and unmarried sister. The kohen gadol (High Priest) may not attend the funeral even of his closest relatives. Certain marital restrictions are placed on the kohanim. The nation is required to honor the kohanim. The physical irregularities that invalidate a kohen from serving in the Temple are listed. Terumah, a produce tithe given to the kohanim, may be eaten only by kohanim and their household. An animal may be sacrificed in the Temple after it is eight days old and is free from any physical defects. The nation is commanded to sanctify the Name of G-d by insuring that their behavior is always exemplary, and by being prepared to surrender their lives rather than murder, engage in licentious relations or worship idols. The special characteristics of the holidays are described, and the nation is reminded not to do certain types of creative work during these holidays. New grain may not be eaten until the omer of barley is offered in the Temple. The Parsha explains the laws of preparing the oil for the menorah and baking the lechem hapanim in the Temple. A man blasphemes G-d and is executed as prescribed in the Torah.
"Until the morrow of the seventh week you shall count" (23:18)
Staying up all night doesnt sound very religious, but there are several times during the Jewish Year when the custom is to burn the midnight oil until the sun peeps through the blinds.
Many people stay up after the Seder on Pesach until the time of the morning prayer to recount and analyze the great miracles of the Exodus. As the Haggada itself says: Rabbi Eliezer, Rabbi Yehoshua, Rabbi Elazar ben Azaria and Rabbi Akiva stayed up all night talking about the Exodus until their talmidim (students) came to tell them that it was time to recite the morning Shema Yisrael.
On Yom Kippur, those with sufficient strength stay up all night in prayer and supplication atoning for their sins. On Hoshana Rabba, the time when the decrees of Yom Kippur are given over to those agents who will carry them out, there is a tradition to learn all night.
On the night of Shavuot too, there is a widely observed custom to stay up all night. The Sages of the Kabbala formulated an order of study call a tikkun (lit. "fixing") for the night of Shavuot. This includes passages from the written Torah, the oral Torah, the mystical Zohar, as well as a list of all 613 mitzvot.
The Zohar commends those who stay awake in anticipation of receiving the Torah. The giving of the Torah was, as it were, the wedding of the Jewish People and the Torah, and so it is fitting that we should be engaged in preparing the ornaments of the bride the previous night.
Another reason: On that first Shavuot morning, there were some who overslept and had to be awoken to receive the Torah. In order to rectify this, we stay up.
But there is a deeper reason that we dont sleep on the night of Shavuot.
Sleep is the taste of death.
If fact, the Talmud tells us that sleep is 1/60th part of death. One part in 60 is the threshold of perception. Similarly, Shabbat is a "taste" of the World-to-Come. Its precisely 1/60th of the World-to-Come.
Sleep is the taste of death in this world. King David died on Shavuot. But before he died, he never even tasted the taste of death, because he never fell into a deep sleep. Thus on the occasion of his yartzeit the anniversary of his death we avoid the "taste of death" by staying up all night.
The angel of death came to King David to try and take his life. But it had no power over him for he was immersed in learning Torah and Torah is the essence of the life-force in this world. The only way that the angel of death could take Davids life from him was through cunning: He managed to distract David from his learning, and in that split second, he was able to take his life from him. So on this night of Shavuot, which is both the anniversary of the giving of the Torah and the end of King Davids life, we stay awake all night and immerse ourselves in Torah study.
Torah breathes life into Man. But it was not always this way. When G-d first created Man, he was animated by G-ds utterance: "Let Us make Man". It was the power of these words spoken by the Creator that gave Man the ability to live and breath and think and act.
However, this was only until the Jewish People stood at the foot of Sinai. When Hashem said "I am Hashem, your G-d" the first commandment the life-force that animated Man parted from the body and the entire Jewish People died. Miraculously their souls were put back into their bodies, but what animated them now was a different utterance. No longer their life-force derived from "Let Us make Man." Now they were like new creations. Their inner essence was powered by "I am Hashem, your G-d." From this moment, the Torah became the animating dynamic of the Jewish Soul.
And when the Mashiach, the scion of King David, arrives to herald the era of the revival of the dead, it will be the Torah, the dew of life, which will be the mechanism to awaken the body from its long sleep.
Then we will finally understand the words we have sung for so long:
"David, Melech Yisrael, chai vkayam!"
"David, king of Israel, lives and endures!"
- Sources: Tehillim 73:5, Yalkut Shimoni; Talmud Berachot3b; Tehillim 19:9; Book of Our Heritage, Rabbi Eliahu Kitov, translated by Rabbi Nachman Bulman; Time Pieces, Rabbi Aaron Lopianski