As a practical matter, true sharpness means effortless cutting; there should be no sensation of resistance when cutting most foods. For instance, a knife which "falls through" an onion, is really sharp. Similarly, even very ripe tomatoes should not need a "starter" puncture to get the cut going and should slice cleanly using the weight of the knife, only. That degree of sharpness is not necessarily extremely sharp, but it's at least truly, and usefully sharp.
With some practice you can get at judging sharpness using "tests" like a thumb drag.
Factory, aka "OOTB" edges can be, are as sharp as most peoples' knives ever get, but they aren't necessarily, truly sharp. People just starting out usually reference the factory edge; but after developing some proficiency, comparisons become self-referential.
Any knife made from decent alloy and with decent face and edge grinds can be made truly sharp. All it takes is skill, patience and decent tools. Of those three things, skill and patience are the more important, while tools are more fun.
Assuming reasonably good geometry (the grinds), all you need to do is create a burr on both sides of the edge using a medium-coarse stone, chase it well (so it flops from side to side with one stroke on the stone), and deburr. If you want a really sharp, fine edge; then repeat the process using a medium-fine stone.
For a finer, more slippery edge, you need to polish. While polish is very nice it doesn't make a knife sharper -- at least not the way I reckon sharpness.
Sharp edges are fairly fine, true and narrow. I don't consider edges which are too "toothy" (the opposite of fine) to be truly sharp because they act like saws more than knives, and as the teeth bend and break, which they do fairly easily, they become more toothy still. In terms of width, a really sharp edge is no wider along its length than somewhere around 2/1000."
While measured edge width (lots of luck finding someone who can do it for you) is "objective," there's also perceived sharpness. Edges which are out of true, may be both fine and narrow, but will not act sharp; and that's where your steel or strop comes in. Similarly, more acute angles and thinner blades will "act" sharper, than more obtuse geometry and thicker blades.