If Valiant ever elaborated on the meaning of the subtitle Children of the Eighth Day, I haven't run across the explanation. It's straightforward enough I suppose, based on the biblical notion of the seven-day cycle, with the Eighth Day thus implying the death or destruction of the last cycle and the rebirth of the new. In recent decades, the term Eighth Day has been used to represent what comes after nuclear (or other kinds of) armageddon. All of which makes the subtitle of this collection of Harbinger #1-4 perhaps another way to say Children of the Atom. Given that Harbinger is about kids with emerging powers of various kinds finding their place in the world, that would be appropriate. A low-print-run variant of the collection of the first four issues of the original Harbinger series, there's a copy of Harbinger: Children of the Eighth Day #nn Blue Variant Cover (Valiant, 1992) CGC NM/MT 9.8 White pages up for auction in the 2021 September 26-27 Sunday & Monday Comic Books Select Auction #122139 from Heritage Auctions.
Familiar as that seems, Marvel's X-Men is hardly the first fiction to tackle such themes, and Wilmar Shiras's critically acclaimed 1953 novel Children of the Atom is directly on point here. That novel was an expansion of the author's previous short stories from Astounding Science Fiction, and like the title itself, had a plot that sounds very familiar to us today: children born to parents exposed to atomic radiation have become Mutants, and are brought together in a secret school for such gifted children where they can explore their unique powers away from a world that would probably shun and fear them. Of course, Children of the Atom was in turn influenced by the 1936 novel Odd John — the story that coined the term Homo Superior.
As for the meaning of the Blue Bird emblem on this variant edition, it's the symbol of the Harbinger Foundation and ultimately of Harbingers themselves. Likely a symbol of the meaning of the word "harbinger" being a forerunner, or more specifically in this case — flying ahead. According to the Valiant Comics Database, the Blue Bird variant was available exclusively through the Diamond Star System and had a print run of perhaps 10% to 20% of the standard edition. A low-print-run variant of important Valiant material, there's a copy of Harbinger: Children of the Eighth Day #nn Blue Variant Cover (Valiant, 1992) CGC NM/MT 9.8 White pages up for auction in the 2021 September 26-27 Sunday & Monday Comic Books Select Auction #122139 from Heritage Auctions.
Harbinger: Children of the Eighth Day #nn Blue Variant Cover (Valiant, 1992) CGC NM/MT 9.8 White pages. Trade Paperback collecting Harbinger #1-4. Jim Shooter story. David Lapham and John Dixon art. Overstreet 2021 NM- 9.2 value = $15. CGC census 9/21: 8 in 9.8, none higher.