7 = 8

The parsha starts by saying the preparation of Aharon and his sons was done on the eighth day.  The Kli Yakar is bothered why is it called the eighth day indicating it continues after a previous seven.  The first seven days were the days of preparing the Mishkan for the service in it and the eighth day was to prepare the Kohanim, a seemingly separate idea?  He explains that seven is the completion of tevah and the eighth day always represents that which is above tevah, kedusha.  The Shechinah coming to rest in the MIshkan was an above teva experience, hence the Torah says it happened on the eighth day because it was eight, kedusha that represented the event that was happening.  However, this explanation seems difficult, for the number eight indicates it is a continuation of seven, however according to the Kli Yakar eight is completely separate from seven? 

The Rebbe (Likutay Sichos volume 3) explains that only after the completion of our service of Hashem in its entirety, represented by seven do we become ready to accept eight.  It is only after man has completed his service to its nth degree that a person becomes ready to accept the kedusha of eight.  It was only because of the avodah done on the first seven days that the Shechinah can come to the Mikdash on the eighth day.   The Nesivos Shalom says that in Shabbos itself, besides being the completion of tevah, there is also an aspect of eight to it.  Through completing our avodah of seven, we are able to reach to the level of eight in Shabbos as well.

The same idea is found in sefiras ha’omer.  The Torah says תספרו יום  but we count only to 49.  We do our max effort which is to reach the 49 gates of wisdom.  Once we have completed our avodah to its fullest extent, then we are given the שער נ' as a free gift from Hashem.