What the numbers on sandpaper mean
Grit sizing, and choosing a sequence that actually saves time.
The number printed on a sheet of sandpaper is a grit rating tracing back to the mesh it was sorted through during manufacture, so a low number like sixty means the abrasive particles were coarse enough to pass through a screen with only around sixty openings per inch, and a high number like four hundred means they were fine enough to fall through a screen with roughly four hundred much smaller openings across the same inch.
What is really going on
Sandpaper is made by coating a backing sheet with abrasive grains, and those grains are sorted to a consistent size before they are ever glued down, historically by passing the crushed abrasive material through a sieve, or mesh, of a specified number of openings per linear inch. A coarse, low-number grit like sixty has passed through a mesh with wide, sparse openings, letting through comparatively large particles that cut fast and remove a lot of material with each stroke, but leave correspondingly deep scratches behind. A fine, high-number grit like four hundred has been sorted through a mesh with narrow, closely spaced openings, letting through only much smaller particles that cut slowly and remove far less material per stroke, but leave scratches so shallow they start to look smooth to the eye and the touch. Because the numbering describes a mesh count rather than a particle size directly, the relationship is not straightforward, doubling the grit number does not simply halve the particle size, since the openings in a fine mesh are packed far more densely and shrink faster than the number itself suggests.
The sieve comparison
A kitchen sieve or a tea strainer demonstrates the same relationship between mesh and particle size directly. A coarse colander, with wide holes spaced well apart, lets chunky pieces of food through easily and quickly, while a fine tea strainer, packed with many more, much smaller holes across the same area, only lets through the finest particles and takes noticeably longer to pass the same volume of material through it. Sandpaper's grit numbering came from exactly this kind of sorting screen, so a low grit number really does correspond to a coarse, wide-holed mesh, and a high grit number to a fine, densely packed one, in the same way a colander and a tea strainer sort flour or crumbs by size. Nobody expects a tea strainer to pass a chunk of vegetable, and nobody should expect a fine grit to remove a deep scratch either, since both are doing the same job of only letting through, or only cutting with, particles small enough to fit the opening they were sorted through.
The number that matters here
Moving from an eighty-grit sheet to a four-hundred-grit sheet is not a modest four-and-a-half-times step in fineness the way the numbers alone suggest, because a mesh with roughly four hundred openings per inch has openings many times smaller in area than one with roughly eighty, so the jump in actual particle size, and in how much scratch depth the finer grit can remove, is considerably larger than the numbers printed on the packet imply.
What follows from this
Because each grit can only remove scratches roughly as deep as the previous grit left behind, skipping too large a jump in the sequence, going straight from an aggressive eighty-grit to a very fine four-hundred-grit, leaves the coarse scratches from the first stage largely intact, since the fine grit simply cannot cut deep enough to remove them and instead just polishes the tops of grooves it cannot reach the bottom of. Working through a graduated sequence, each grit only a few steps finer than the last, costs more total sanding strokes but actually finishes faster, because every stage is capable of fully erasing the marks the previous one left, rather than leaving a smooth-looking surface with deep scratches still hiding underneath a thin, polished skin. A useful check partway through a sequence is simply changing the direction the sanding strokes run with each new grit, since scratches left by the previous, coarser grit then show up clearly, crossing the new direction, right up until the finer grit has genuinely erased them rather than merely glossed over their tops.