The parashah Naso, this week's Torah portion, is always read before or after the festival of Shavuot. Our sages explain that order in the Torah is Torah itself; that is, to paraphrase the famous mathematical principle, in Torah, the order of the factors alters the product. For some reason, God determined that one event should occur in close proximity to another. That very thing is a "product" of Divine wisdom.
In this case, the eternal proximity of parashat Naso with Shavuot leads us to look for what the connection is between these two matters.
Shavuot is the festival of the Giving of the Torah. While our patriarchs Abraham, Isaac, Jacob, and their descendants studied Torah, their study had no effect on the material world. On Shavuot, God broke down the barrier separating the material from the spiritual and allowed us to imbue the world with holiness and purity through the Torah.
Now, the idea of refining the world does not apply only to what is external to the person; it is not enough to use the objects we encounter in life for a holy purpose, but the work also consists of refining oneself, and, even more, the beginning of the work is with oneself, in order to then spread that holiness that emanates from the person to affect the world in a positive way.
And this is where we see the connection between Shavuot and Naso. The word Naso means to lift up. God commands Moses to count the sons of Gershon, one of the sons of Levi. The expression he uses is Naso, literally "Lift up," says God, "the heads of the sons of Gershon." The connection lies in the fact that the study of Torah, that Torah given on Shavuot, should not be merely an object of intellectual development, an object of study, but rather it should lift (Naso) the person, take them out of their previous state before the study and place them in a new, better, more refined position than before.
In other words, true Torah study means that, after the study, the person should have changed, should be a better person, both for themselves and for the rest of the world. If this did not happen, the study was not entirely appropriate.
As the Baal Shem Tov used to say, one should learn a lesson from everything one sees and hears in service to God. The same applies to Torah study; one should extract from one's study something that elevates one's level and makes one a better person, better equipped to make the world a dwelling place for God.