From the Rebbe’s explanations:
– The number 27 is equivalent to the word “zach” (זך), meaning “pure,” as in the Torah phrase:
And you shall command the children of Israel, and they shall take to you pure olive oil (“shemen zait zach”), crushed for lighting, to kindle the lamps continually (Tetzaveh, 27:20).
This is a kind of an oil which produces an especially bright light.
Thus the 27th of Nissan reflects the idea of revelation.
In Nissan, the month of Geulah, the light of Redemption will be brightly revealed.
The number 27 is also significant in that it is three times nine. Three is associated with the concept of chazakah, a threefold sequence associated with strength and permanence:
… The presumptive status [of a phenomenon] – chazaka – is established by three occasions (Bava Metzia 106b, according to the opinion of Rabban Shimon ben Gamliel).
Nine is three times three, so 27 is a further multiple of three. Meaning that the number 27 represents a double chazakah – chazakah in regard to chazakah…
From the Rebbe’s talk on the Eve of 28 Nissan, 5751. Free translation.