What does "The Space of Potential Meaning" mean when talking about Genetic Structuralists Theories?

This is a metaphorical description or explanation, a sort of analogy, which places meanings as a volume of space that is covered by the word or phrase or concept. You probably should think of it in terms of sets in three dimensions, with meanings having bubbles that sometimes overlap, and even when a meaning often has an ill-defined limit (the edge of the bubble is not clearly defined) there are still zones that are clearly WITHIN the space of meaning (within the bubble) and OUTSIDE of the bubble (not part of the possible intended meaning.

In other words, the person is speaking of meanings, concepts, and structures as if they were real space, even though it obviously is not REAL space that such things occupy. It is a conceptual, an imagined, space, a way to image the ideas in ways that our mind is familiar with from reality.

The specific idea of that phrase is that, right from the outset, there are limits to what can be included in the meaning (what can be included is what could be called POTENTIAL meaning, as opposed to not at all possible meaning).

'Potential' means 'could be' or 'could happen', and in some ways it is as big as the entire universe, because it hasn't been defined or limited ... yet. It sounds from your quote and context that putting a 'conceptual structure' there does two things: it both creates and restricts the space that is there and which has potential. Creating and restricting are ideas that are related to defining and limiting as this whole process goes along.