The second part of the verse "וְעַל-פְּנֵי כָל-הָעָם אֶכָּבֵד" explains the effect of the cause of "אֶקָּדֵשׁ" with "אֶכָּבֵד" the parallel is the use of the same number of letters and same vowels. The root of "אֶכָּבֵד " is "כבד" and it is related to a revelation or "גילוי" in Hebrew. The numerical value of the root is 26, which is the value of the name "יקוק". The action of "קדש" cause "כבד" or "כבוד" and the revelation of the Light as it say in Vayikra (9:6)
"וַיֹּאמֶר מֹשֶׁה, זֶה הַדָּבָר אֲשֶׁר-צִוָּה יְהוָה תַּעֲשׂוּ–וְיֵרָא אֲלֵיכֶם, כְּבוֹד יְהוָה. ",
in (Ezekiel 43:4) "וּכְבוֹד יְהוָה, בָּא אֶל-הַבָּיִת", (Exodus 16:7) "וּרְאִיתֶם אֶת-כְּבוֹד יְהוָה" and in many other places.
Nadav and Avihu made a great revelation of light that Moshe and Aharon understood. It said (10:3) "וַיִּדֹּם אַהֲרֹן", And Aaron held his peace.
Every Yom Kippur we read from the story and the scarify of Nadav and Avihu from the parasha of Shemini. Yom Kippur is a day of total connection to Binah (We do not eat on that day so our bodily desires won\’t interfere and ground us when drawing the spiritual energy of Binah).
The Ari HaKadosh explains that they wanted to make the correction of the sin of Adam and complete the correction of the world "Tikkum Olam".
Commentaries explain that the fire to burn the sacrifices for Aharon and the Nation came from inside the Tabernacle. When Nadav and Avihu saw the Light of the creator so close to them, they assumed that they had the power, as Kohanim to make the final connection of the Light to the world and remove all negativity. The Ari said that they made few mistakes and they couldn\’t succeed in achieving their goal. This doesn\’t take the value from their action that left us with channel for all generations. Another famous selfless act was done by Miriam the Prophetess and gave us a healing connection. (B"H in another article).
Their death was unique because their body stayed complete when the fire from G-d took their soul like the fire that comes down to burn the sacrifices.
Later we read in the Torah in Parashat Ballak about Pinchas the Kohen doing an extreme act of killing the head of the tribe of Shimon in order to stop a plague that invaded the camp of Yisrael. The Zohar explains that after he killed Zimri, the people of his tribe came to attack Pinchas and out of fright, his soul went out of his body and got replaced by the soul of Nadav and Avihu, his uncles. This also explains why Pinchas could stay as a Kohen after he made the killing. His new soul had no part in the killing. We also know that Pinchas became Eliyahu the Prophet and he never died. We all know the role of Eliyahu Hanavie in every Brit that connects the soul to the Light; He visits us in the Night of the Seder to connect us to the final redemption and will come to announce the Mashiach (B"H today, Amen.)
Parashat Shemini has 91 verses and as we showed earlier it is the gimatria value of Nadav and Avihu. The parasha also has the middle of the Torah in double letters (10:16) "דָּרֹשׁ דָּרַשׁ" and the middle of the Torah in Letters (11:42) with the Large letter "ו " that we know is the letter that channels the light of the Torah as it appears at the top of every column in the Torah (except for 6 special places) and its size makes a bridge to Binah.
Please read this article several times to get better understanding of the higher connection we get this Shabbat from the Torah reading of Shemini.