Our portion this Shabbat is named after a significant number in Jewish life, the number "Shemini", Eight! Eighth day of circumcision, Eighth Day of Solemn Assembly, Eight Days of Chanukah, Eight Laws of Tzedakah of Maimonides, and this week's Eigth Day following the inauguration of Aaron the High Priest and his sons.
This is a day of special holiness symbolic of a path of holiness which the Kohanim and the Israelites were to follow until the end of time.
As a Holy cloud had previously descended to surround the Tabernacle signifying G-d's presence, so now on the Eighth Day a Fire had descended to consume the offerings on the altar to signify the Divine presence. Unfortunately, and to Aaron's horror, his 2 sons Nadav and Avihu were stricken with sudden death because they offered a "strange fire" to G-d which was NOT commanded by Him. There is a great lesson to be derived from this, not that G-d forbid we will be stricken by a bolt of lightening if we violate G -d's law, but rather that we remain keenly aware of keeping G-d's commandments in our everyday lives. Thus follow the extremely detailed laws of KASHRUTH of what we consume in our bodies. We are to be a Holy People, distinguishing the creatures and foods that we are permitted to consume and not permitted to consume. This all ties in with the laws of PURITY and the Mikvah which are also enumerated at the conclusion of the Parasha. Purity is the hallmark of this portion, and in most years is read at Passover time, held in suspension because of the special readings for Passover.
In conclusion, we are to remain a distinguished and a distinguishable people through the laws of Kashruth and Purity for the entire world to see and learn from. Whatever we may not understand, we may then use the concept of the Eighth Day of Perfection, that which we accept on Faith and which much of the time is beyond our natural human limitations.