Fine stones for the last passes
A burr is the material that builds up when one side of a blade is sharpened, as Buck's Journal post puts it: "the material will build up creating a burr." Gerber's how-to checks for one by running a thumb gently across the edge; Buck's how-to page is not done until the burr is gone from both sides.
Buck's Journal post says the material builds up into a burr as one side is sharpened. Buck's how-to has you pat or wipe the knife dry after the coarse stage, carefully, because "the burr can cut just like a sharpened edge." A burr can also pass for a keen edge: Böker USA says a burr can be felt and is often mistakenly taken as sharper, while the sharpness of a fine-grained, burr-free blade is almost impossible to feel.
Gerber's whetstone how-to says that after "anywhere from 30 to 40" strokes a burr may develop; you check by running your thumb gently across the edge, and if it catches, it is time to repeat on the other side. Buck's how-to page says not to alternate sides with each stroke, because that makes it harder to keep the angle or find a burr. In Stage 3, Buck's how-to still expects a burr, "smaller and finer," once the previous grit's scratches are gone.
In Buck's Journal post, the burr comes off with one more flip of the knife and one last pass. Buck's how-to page takes it off with light, single strokes from side to side until neither side has a burr to feel, then, in Stage 3, one stroke per side, hilt to tip, until there is no burr, which "will finally set the edge." Buck's how-to warns that too much pressure can break the burr off and leave new flat spots. How to sharpen a pocket knife walks through the full stone method.