Seven is the number of nature in the Torah (as the world was created in seven days). But the number Eight is used to connect man and G-d. So we have the circumcision on the eighth day (Gen. 17:12 and 21:4), as well as the offering of the first-born animal (Ex. 22:29) on the eighth day. Similarly, after seven days of inauguration of the priests, it was on the eighth day that the priesthood was consecrated and started the active service between man and G-d (Lev. 9:1). Many sacrifices and festivals that were involved with establishing a connection between man and G-d were also called for the eighth day.
Hebrew is a language with relatively few words, and so different words often share a common root. In the case of “eight” the word is composed of three letters: shin, mem, and nun, which spell shemen, or oil. And what is very cool (at least for a Torah geek like me) is that the very first time oil is mentioned in the Torah is when Jacob, after awaking from the dream in which he sees angels ascending and descending from heaven, announces his realization that the place is the “gate of heaven.” (Gen 28:18). Jacob takes the stone that he had used as a pillow, the resting place for his soul the night before, and sets it up as a pillar. Then, to seal the deal, Jacob poured oil on top of it.
This is not only the first time oil is mentioned in the Torah; it was also the first time anything is poured on any head. But it was not the last! Jacob actually seems to set the trend. G-d commands Moses to pour oil on Aharon’s head (Ex. 29:7), which he does (Lev. 8:12). (The language is the same in all three cases.)
There is reciprocity here. Jacob connected heaven and earth in the place where he experienced his dream, and he used the pouring of oil on the head of his pillar to seal the connection. So when it was time for the priests to be consecrated as the intermediaries between the Children of Israel and G-d, then they were annointed with oil
Why oil? Perhaps we can say that oil was the embodiment of the relationship between man and G-d, the meaning of the number eight, with which it shares the letters.
The natural world can be represented by a vegetable, but the creation of oil requires both nature and man’s effort to extract the essence of the vegetable. Oil is thus an amalgam of both divine creation and mankind’s investment of time and energy. The end product is highly nutritious and energy rich, usable as a food and fuel. In the Tabernacle and Temple it was used for both: an ingredient in edible offerings, as well as to light the menorah (the Chanukah version of which has eight lights).
So for Jacob to pour oil on the altar was to both acknowledge the natural bounty that made oil possible, as well as to expressly connect mankind’s refinement of that bounty and its investment into the relationship between man and G-d.