This week's section is called Naso (counting). God continues to command Moshe to count the sons of Levi, one of the twelve tribes of the Jewish people.
Our sages say that we always read the Bamidbar section (from last week) before the festival of Shavuot (which occurred this week). It follows that we always read the parashah Naso after Shavuot, Naso being the parashah Following Bamidbar. Obviously, there must be some connection, not only between the Bamidbar section and the Giving of the Torah, but also with Naso; nothing is a coincidence...
Our sages explain that one of the most important aspects of the Giving of the Torah is the union of the spiritual with the material. Before the Torah was given, the concept of a mitzvah as a divine commandment already existed, as God instructed Abraham to be circumcised, and He transmitted certain precepts (such as Shabbat and economic laws) to the Jewish people even before the Giving of the Torah. The novelty of Shavuot is that each person was given the ability to unite the material world with the spiritual—in other words, to imbue the mundane with holiness, to bring God to earth through the observance of His precepts.
That's where the parashah This week's text. Naso doesn't just mean count. When God commands Moses to count the people, He literally tells him to "elevate," that is, to raise the count of the people and see how many there are. But, from a deeper perspective, to elevate means to lift something that is low. The text of the parashah According to this new interpretation, it says, “Lift up the heads,” instead of “count the heads.” This idea of lifting up the heads signifies, among other things, raising the spiritual level of the Jewish people. Of course, the elevation and refinement of “the head,” the intellectual, is achieved through study.
Hasidism explains that there is a very strong relationship between a person's intellect and their emotions, such that the intellect governs and develops the emotions. The idea of raising one's head, then, is directly related to the elevation and refinement of the emotions.
The Giving of the Torah, then, is the step prior to our being able, through its study, to raise our heads, our intellect in the understanding of what God allows us to know of Him through His Torah, so that we can, consequently, elevate our emotional qualities and be better people, to reveal the Divine presence on Earth and make a worldly space into a holy one.