Distinctions
In contradistinction to the rest of the week, Shabbat is a holy day. Though the weekdays lead up to Shabbat and are influenced by Shabbat, they can never become holy; they are forever destined to be mundane. With one 
Can the weekday ever become sacred by its proximity to Shabbat?
exception: the festivals.
The Jewish festival is an odd phenomenon. On the one hand it is a holy day, on the other hand it often falls on a weekday. The festival transforms an ordinary weekday into something of a holy day. When a festival falls on Monday it is no longer mundane; it becomes holy. With few exceptions, we abstain from worldly actions and entanglements and focus exclusively on the commandments, the Torah and G-d.
Yet, in some ways, even on the festival Monday remains an ordinary weekday. When the festival ends and the ordinary weekday begins again, Monday's holiness will dissipate and, in the next week, will be as mundane as it was in the past.
Is there any way to channel the holiness or G-dliness of Shabbat and the festivals into the rest of the week? Can the weekday ever become sacred by its proximity to Shabbat?(1)
The Eighth Day
To bridge the gap between the festival and the weekday it was ordained that Passover (at least outside of Israel) and Sukkot extend for eight days.(2) The number seven represents the order of creation: G-d created the world in six days and on the seventh day He rested. Six days for creation and the seventh for G-d. This is the realm of demarcation and limitation; where holy and mundane do not mix.
Eight represents a metaphysical order that bridges the two. The cycle of the week is confined to seven days. It cannot overcome this limitation and reach the number eight; the moment the seventh day ends the first day returns and the cycle begins anew. Eight thus transcends the entire order of nature; it is a supernatural order; an order whereby G-d is not seen merely as the Creator, but as the essence of all existence. He is the essence of the sacred and of the mundane; He is at the epicenter of the entire human experience, the quintessence of all that exists.
If holiness is measured by proximity to G-d, all of time, space, nature and the supernatural should be considered holy. Does G-d not comprise the essence of them all? Is G-d any closer to one than the other? He is equally distant and equally close to every moment, space and experience. In a sense, they are all equally G-dly. No time is holier than another, no space is more G-dly than another, and no person is more significant than another. We are all equally important, for we are all equal expressions of the Divine. This universal equality is expressed by the number eight.
The message in the eighth day of Passover is that the holiness of the week does not end with the conclusion of the festival. The festival appears to be a holier day than the day that follows it, but the essence of all days is equal. Every day is conducive to holiness. The experience of every day can be G-dly. Indeed, it is possible to channel the additional measure of reverence that we experience on Passover into the rest of the week and year.(3)
G-d on Earth
This is why it is of particular interest that the Torah portion of Shemini is often chanted on the Shabbat following the eighth day of Passover.
Shemini means "the eighth". This Torah portion speaks of a seven day training period enjoyed by the priests and Levites before the Tabernacle was formally inaugurated on the eighth day. That G-d chose to inaugurate the tabernacle, the home for the Divine on earth, on the eighth day is of significance.
The Tabernacle telegraphed to all humankind that holy thoughts, feelings and experiences are not the exclusive domain of holy places and times. No matter the circumstances, every person is capable of living a G-dly life. We might find ourselves in a fog of emotional uncertainty, plagued by feelings of inadequacy, haunted by a lack of confidence or crushed by repeated failure; and yet it is possible to succeed. We might experience black yearnings or dark cravings, we might be gripped by jealousy or anger, malice or malevolence, and with such thoughts coursing through our minds, such feelings pulsing in our heart, we might consider ourselves unfit for refinement and G-dly transcendence.
The message that G-d sent when He instructed us to build a tabernacle is that every place can be a home for G-d. The throbbing metropolis and the barren desert can both serve as a suitable domain for the Divine. To accomplish this, all that is needed is that we erect a tabernacle and set up its sacred vessels. Every heart can be a tabernacle. Every person can be a home for G-d. All that is required is that we turn our thoughts from self-serving concerns to the wishes of our Creator. No person is beyond the pale. No place is too unholy. Everything was created by G-d. Everyone can serve G-d.
It is of particular interest that the Torah portion of Shemini is often chanted on the Shabbat following the eighth day of Passover.
This is why the Tabernacle was inaugurated on the eighth day. This is also why Passover ends on the eighth day.(4)
This is the message of the eighth day. Can we live up its challenge?
Footnotes
1) One would suppose that the intermediary days of the festival accomplish this task. They are days that combine the holy and the mundane. During these days most actions forbidden on festival days are permitted, yet these days are graced with unique holiday traditions. Here we have a seemingly ordinary weekday, graced with a measure of holiness.
Still, even this is merely a temporary transition from the usual. When the holiday concludes we return to the ordinary routine of the mundane. Shabbat is holy; the rest of the week is not. Shabbat is a day for G-d; the rest of the week is simply not conducive to holiness.
2) This is, of course, the mystical reason for this extension. The Halachic reason for the extension is rooted in the methods by which the Hebrew calendar was determined in the ancient times. The mystical reasons were articulated by the Chassidic masters and by Kli Yakar on Leviticus, 9:1.
3) To a small degree this is experienced on a weekly basis on Motzaei Shabbat - Saturday night. The night is aglow with the aftereffect of Shabbat, yet it belongs to Sunday; it is a weekday. This is why Chassidim in particular place great emphasis on partaking in a festive dinner on this night. The dinner is called Melave Malkah - "accompanying the (Shabbat) queen". It is also called Seudeta DeDavid Malkah Meshicha - "the feast of David, King Messiah". For further elaboration on the number eight and Moshiach, see the next footnote.
4) This is why Moshiach's harp will contain eight strings, in distinction to King David's harp that contained only seven. The Temple conceived by King David and built by King Solomon was indeed a home for G-d, but it was erected in an era of the natural order. It was only within the Temple compound that the supernatural was palpable, the rest of the world could discern only the natural order of seven. The Messicanic era will usher in a new epoch. In this time, the entire world will be filled with the glory of G-d and our Creator will no longer be concealed from our vision. At that time, the whole of the world will pulse to the rhythm of eight. For further detail see Kli Yakar cited in footnote no. 2, as elucidated in Likutei Sichos XVII p. 93.