I think this statement of Cat's is rather profound. It meets the question of "What's Outside" by putting it in the context of the ability to directly perceive their space (Is it 1D, 2D, or 3D). The higher-dimensional being can always resolve the dilemma of what is outside.To the Flatlander, it is "infinite" (having no boundary).
His "universe" is a spherical surface.
If you prefer the version where the surface represents spacetime, then there is no end to space or time (to put it in those terms.
If you prefer the version where the surface represents space (2D) only, then he can perceive no time limitation - the surface may expand 'in time' in this version.
But to the D+ observer, the Flatlander's "universe" is easily perceived as bounded, and for D+ there could be any number of Flatlander "universes".
The Flatlander perceives expansion of his "universe" by noticing that distances on his sphere grow larger. He senses expansion, but does not know into "what?".
The D+ observer perceives expansion of Flatlander "universes" by noting the "radius" of the expanding Flatlander spherical surface "universe". This "radius" is incomprehensible to the Flatlander, but D+ can see any number of them, whereas the Flatlander believes that he is alone.
The 2D Flatlander cannot conceive of the radius of a sphere and therefore cannot understand the inside space (cannot conceive of a ball) and of course, the inside of the sphere is the same 'type' of space as the outside of the sphere into which the sphere can grow.
In a similar way a 3D flatlander (let's call it a Spacelander) has trouble with the idea of what is outside our universe.