The quoted sentence is an informal description of "positive density", and you can find the definition of density at https://en.wikipedia.org/wiki/Natural_densit

The quoted sentence is an informal description of "positive density", and you can find the definition of density at https://en.wikipedia.org/wiki/Natural_density https://en.wikipedia.org/wiki/Natural_density, or you can take a look at the first page of the source material at https://arxiv.org/pdf/2112.03726.pdf https://arxiv.org/pdf/2112.03726.pdf. In fact, the theorem proved works for a stronger notion called "positive upper density"; the definition of "upper density" is also in the linked Wikipedia page.