Think of a cylinder whose radius is of atomic size. More or less that is what they mean.
That space is “felt” as 1-dimensional because there is no way to tell one point on a circumference from another on the same one.
That space is “felt” as 1-dimensional because there is no way to tell one point on a circumference from another on the same one.
The tricky variant is when the compact dimension is seriously sub-atomic, so you have trouble moving anything easily detectable along it.