Night Torah as preparation for Kabbalas HaTorah

בענין הלימוד בליל החג הוא על פי דברי הינוקא בפ' בלק בפי' עושי דברו ע"ש ולכן ע"י עסק התורה בלילה כביכול מוסיפין כח כדכ' תנו עוז כו' והוא עצמו מ"ש בזוה"ק בהקדמת בראשית דנקראו פועלי צדק.

Regarding the custom of learning on the night of the Yom Tov (the Tikkun Leil Shavuos): it is based on the words of the Yenuka (the wonder-child) in Parshas Balak in his explanation of "doers of His word" (Tehillim 103:20) — see there — and therefore through engaging in Torah at night one, as it were, adds strength, as it is written: "Give strength to God" (Tehillim 68:35); and this is the very same idea taught in the Zohar HaKadosh in the introduction to Bereishis, that they are called "workers of righteousness."

Learning Torah on the night of Shavuos draws on the Zohar's teaching that those who fulfill Hashem's word — His "doers" and "workers of righteousness" — actually add spiritual strength on High through their nighttime Torah, becoming partners in upholding the world.

וזוכין ביום לשמוע בקול דברו.

And in the day they merit "to hear the voice of His word" (Tehillim 103:20).

Having toiled as the "doers of His word" by night, on the day of Shavuos they rise to the higher level of "hearing the voice of His word" — receiving the Torah directly.

וע"י התחברות באסיפות חברים כדכ' בזוה"ק לית מאן דידע לקשוטי כחבריא וכדכ' ברוב עם הדרת מלך.

And this comes through joining together in gatherings of friends, as it is written in the Zohar HaKadosh: "there is none who knows how to adorn (the Shechinah) like the company of friends," and as it is written: "in the multitude of people is the King's glory" (Mishlei 14:28).

This avodah is accomplished specifically in groups — chavrusos and assemblies of Torah learners — for the collective study of friends "adorns" the Shechinah and reveals the King's glory more than solitary learning.

ובכל ימי הספירה הוא ג"כ הכנה להחג בבחי' עושי דברו:

And throughout all the days of Sefirah (the Counting of the Omer) there is likewise a preparation for the Yom Tov, in the aspect of "doers of His word."

The entire Sefiras HaOmer period serves as a gradual preparation for Kabbalas HaTorah on Shavuos, the days themselves being the avodah of being "doers of His word" leading up to the moment of "hearing the voice of His word."

Summary: Learning Torah on the night of Shavuos fulfills the role of being "doers of His word," which the Zohar says adds strength on High, so that by day one merits to "hear the voice of His word" and receive the Torah. This is best achieved in the company of fellow learners, who together "adorn" the Shechinah, and the whole period of Sefiras HaOmer is itself a preparation for this avodah.