What does it mean that "The prime fact of Negation is its Nothingness" ?

When something is negated it is the misconception of how it is thought to exist that is negated, not the actual way it does exist. So using the hamburger idea, if it is negated, it is the way the hamburger appears to exist. Also, is the hamburger inherently desirable? Or inherently undesirable? It has shape, colour, texture, form, smell etc, and depends on causes and conditions to bring it into existence including the concept that it is a 'hamburger'. But the concept is based on human ideas, and labelling. So even if all the ideas and concepts about the hamburger are negated, there is still something in existence, but what remains is a mere object. Conventionally, there is still something there in existence, just not from its own side. If the hamburger were to be disassembled, where is the hamburger?

UPDATE: The most important point when negating is its product: if a hamburger is negated, then the hamburger is nothinged.

Like surfing: "...wipe out."

What may seem mystical about "Negation is its Nothingness" is a) Capitalization as if Negation were a God, ditto Nothingness; b) "Negation" is equivocal, possibly a noun and possibly a verb or process. As Negation's prime fact is its Nothingness, Negation cannot be a noun, but if considered a "thing," the thing that it is, is a construct, a concept. Negation as a process is simply the process of "wiping out" or consuming the hamburger. Hope this helps; if not, kindly give a second request, pointing to what you're focusing on for additional meaning.

Heidegger here focuses on the nonimplicative negation ("x is not"), which eo ipso = process of negating re x-ness: "x is not."

A "nothing burger" is a nonimplicative negation.

There are other types of negation, e.g. implicative ("x is not of y": "this burger is not an omelet").

Bob Dylan does an extended negating in his frankensteinian (as in Mary Shelley) https://www.youtube.com/watch?v=wMDO_lvSQYE If a "broken burger" is a "nothing burger," then the negating is nonimplicative; if the "broken burger" is an x no longer x because it's broken, but it is a thing ("y"), then the two types of negation, nonimplicative and implicative, blend, and a Wittgenstein or other philosopher of language games is needed--if one is saddened by the confusion of "a broken burger" as both an implicative and a nonimplicative "nothing burger."

Remarkably, Heidegger is perhaps more clearly focused.

Semi-related: "The Soulless One."