The conjecture is geometric. If X is a set containing n elements, its subsets may be considered as the vertices of an n-dimensional cube. For example, if X has three elements, choose any ordering of them, say (a, b, c), and then consider a subset A of X as the coordinates (x, y, z), where:
x = 1 if a is in A, x = -1 if a is not in A,
y = 1 if b is in A, y = -1 if b is not in A,
z = 1 if c is in A, z = -1 if c is not in A.
So e.g. {b, c} = (-1, 1, 1), {b} = (-1, 1, -1), empty set = (-1, -1, -1), X = (1, 1, 1). Totally standard:
Then (A, B, C, D) is a rectangle, as defined above, if and only if the corresponding coordinates are the vertices of a rectangle. The point of the conjecture, if true, is that for any tope T there would exist a hyperplane separating sets in T from sets not in T, thus providing a description of the geometry of the n-cube independent of infinite Euclidean space.
https://en.wikipedia.org/wiki/Hyperplane