What meanings might be conveyed by something being called brand new, as opposed to it simply being called new? What's behind the word brand here?
According to the Online Etymology Dictionary, in Old English the word "brand" carried the meanings of "fire, flame; firebrand, piece of burning wood, torch". The word "brand" comes from the Germanic languages (and Old English was still very much part of the Germanic family) and is still commonly used in modern Dutch and German to mean "fire".
The meaning of "brand new" is thus, as also noted by the Online Etymology Dictionary, "fresh from the fire". I presume the term originally referred to items produced by a smithy, which were molded and tempered by the heat of a fire.
Etymonline suggests "fresh from the fire".
It seems brand is Old English for fire or flaming; the Dutch word brand still means fire in English.
For this etymology to work, we need to know the approximate date of the first usage of the phrase "brand new." For all we know, it could refer to new products under copyright or trademark, as in "brand-name" products, as opposed to generic knockoffs, which by definition are brought to market later. According to Google N-gram, usage of the phrase "brand-new" or "brand new" in print begins in 1870 and picks up in the early 20th century. I think the association of "brand" with property seems right, but its origin and and increased use during a period of dramatically increased patent and trademark issues might also be worth considering.
The expression brand new just intensifies the idea of new. Obviously it is no longer clear where this image comes from, so you can choose any object that is produced by heating as iron pieces and the like. I have chosen the image of a pottery where the pieces are burnt in an oven.
Compound adjectives of the type brand new where the first element intensifies the simple adjective are not uncommon. Unfortunately I have no representative list to hand, only some examples with stone: stone cold, stone dead, stone still
and with dead: dead right, dead wrong, dead straight, dead flat, dead calm, dead drunk. This adjective is not related with death, but with total. My view.
My conjecture is on the lines of branding rather than brand itself. A hot iron or wooden tool was typically used to brand cattle with an identification, could be to indicate ownership. This leads to the idea that something brand new would be like a new member of one's cattle just branded.
By extension, a car leaving the production lines gets its gleaming logo (brand) fixed just before leaving for the market: a brand new car!
The association of brand-new with fire is indeed the right one. To support that claim, consider the rarer, yet synonymic expression fire-new.