This week's Parshah, Shemini, describes events of the eighth day following the seven days of inauguration of the Tabernacle. It was also a day, our sages tell us, which possessed many "firsts": it was a Sunday, the first day of the week; it was the 1st of the month of Nissan, marking the beginning of a new year, it was the first day that the Divine Presence came to dwell in the Sanctuary, the first day of the Priesthood, the first day of the service in the Sanctuary, and so on. With so many "firsts" why does the Torah refer to it—and by extension, to the entire Parshah—as "the eighth day"?
The answer is that the number "eight" defines certain qualities. Seven is the order of nature–-represented in the seven days of the week; eight is "higher than nature." On the other hand, the Torah is connecting this day to the seven days that preceded it–-it is not just a day in its own right, but the "eighth day" following a cycle of seven. This teaches us that an event or concept does not just exist in its own right, but has a link to the preceding events.
Similarly, our generation is compared to "dwarves standing on giants' shoulders"--although we may appear to be on a lower spiritual level (dwarves) than previous generations, the boost we gain from their achievements (the giants) allows us to "stand on their shoulders," reaching a higher level than they themselves could.
We also read in the Parshah about the sons of Aaron who, in their desire to come close to G‑d, sought liberation from their physical body, to be "consumed" by G‑d. It is a reminder that whilst we need a fiery determination and drive for spirituality, this needs to be channeled into our "this-worldly" existence, through mitzvot involving the physical, material world, to elevate our environment around us. It is not achieved by removal from this world, but rather by involvement with all possible aspects of it, in order for the spiritual to permeate the physical.
-adapted from www.chabad.org