Earlier quoted context omitted.
Below the Planck distance, "closer" ceases to be a meaningful concept. Similarly, distances larger than the size of the observable universe may also be meaningless.
Why is that? I've heard this before but don't understand what it actually implies. Like, why can't 2 things meaningfully be half a Planck distance apart?
This is just according to our current theories, and you don't need any speculative ideas about granularity of space. Mathematically, there's no problem in considering arbitrarily small length scales, because current theories are based on continuous space and time dimensions, but since we can't give physical meaning to small length scales, that's a clue that a more fundamental theory will somehow not be based on continuous space and time