I am a novice to JP Sartre's philosophy of existentialism and I came across the notion that in Being and Nothingness,The Origin of Negation where he claims that "nothingness is at the origin of negation". I do however have difficulty understanding this notion. I understand that négatité, being a phenomenon, brought into being only by being-for-itself, can only happen because of the unbound freedom we possess, and that our existence precedes our essence. Is this why nothingness is at the origin of negation? Any help would be appreciated.
Nothing(ness) definitionally is being not Being. It therefore not is, ontologically. It is just that "not", the refusal to be this or that concrete X. Sartre often characterizes for-itself and its activity (choosing, i.e. running from a fact towards a possibility) as "being by mode of non-being".
Nothingness should not be understood as something which is absent here still potentially is present somewhere else (real or imaginary - no matter). Nothing is what is nowhere. Or, rather, it is here as the pure negation/attenuation of any state of identity in "i is X"; that bold "is" is what gets negated. Nothingness emerge (due to human Consciousness making choices) as holes bored through on the body of Being, to attenuate self-identity of things.
Because, for a thing (phenomenon) to have any sense/meaning it must be weakened in its sameness with what it is - for the sake of tying with some chosen possibility. For example, a red ball appears meaningfully "red" to us because its redness is being rejected in exchange of some potentiality in the red quality of the ball. Venus de Milo "has no arms" to us meaningfully only because it could have arms, i.e. be what it is not; however, that "could have arms" is firstly not another state or being, it is the possibility which exists by mode of nothing because it does not change the Venus de Milo to another identity, it just attenuates its present identity by loosening. Only due to that attenuation (negation) of the statue's being without arms it can appear meaningfully as having no arms.
There is nothing (no anything) that separates the Venus as it appears from its identity of Venus armless, yet it is not equal to it. Simultaneously, there is that same nothing that separates it from the possibility of armness, yet having arms is not any guaranteed, even not under consideration. (Nothingness does separates by no miles or millimeters, and it does link by no bridges or molecules.)
Consciousness opens things as phenomena (appearances). That is, it acts as negation and brings nothingness to things. It attenuates a thing's being what it is, due to which the thing can appear what it is. To appear means to be X with potentialities, while being is just to be X - the state of closed and dense identity where no meaning could arise and even the statement "i is X" can't linger as intelligible. Sartre's concept of Nothing/Negation is sharply dialectic, it owes to Hegel.
[why is that] nothingness is at the origin of negation
According to the IEP
The power of negation is an intrinsic feature of the intentionality of consciousness... in... this power of negation... I operate a nihilation of that which is given... Sartre says that 'the name (...) [of] this possibility which every human being has to secrete a nothingness which isolates it (...) is freedom' (BN, 24-25).
So yes, the answer of why it can occur is "freedom".
Obviously, this answer is quite short.