In art, positive-space is the space taken up by a depicted object. Negative-space is the space not taken up by a depicted object. It's the space between objects.
These illusions teach us to respect the negative space as much as the positive space. Either one can be used to define a shape.
Artists use these concepts to break up the symbolic way we see the world. Rather than looking at an eye and then drawing a symbol for an eye, say a football with a dot in it, like the CBS logo, they see the shape of the space around the eye. This helps them draw accurate proportions. So that when an artist sees an eye, they see all it's shapes. Not just, "Hey look, an eye".
Illusions are used to teach this concept to budding artists. For lay people it's just a curiousity.
When looking at ambiguous gestalt illusions your perception may switch back and forth as you perceive the illusion in different ways. There is a term for the switching. It's called:
A visual illusion where perception alternates between two possibilities. A pair of shapes, either of which taken alone would be seen as an object of some kind, share a common border-line.
There is a whole science behind this devoted to the study human perception.
The analogy of breaking the fourth wall isn't entirely misplaced. Negative space can be made as powerful as positive space most strongly in monochrome 2D because this style removes all hints of an object other than shape. This leaves the viewer to fill in details based on impressions.
In a play, the viewer is also asked to fill in details based on impressions. Doing this is part of suspension of disbelief. Breaking the fourth wall is when the actors actively remind you that the play isn't real. It's all pretend. Toying with negative-space to make figures can similarly be used to remind you that the art isn't real.
However, there are illusions that play with negative space made with real 3D objects:
There is no violation of suspension of disbelief here since there is a clear winner, the pillars. The tension doesn't come from ambiguity. It comes from how strongly we recognize the shape of a human over a simple piller. We know the human isn't real but find it more interesting.
Sometimes there isn't even an illusion. You're just being challenged to decide when there is no good reason to pick one over the other.