The demon stands in a room with a blindfold on. It hears footsteps but cannot see the whole room. The demon tries to sort molecules by speed in order to extract work from thermal motion. It used to be thought that the demon sees every molecule and can use all the information. Now it turns out that this is not so.
If the demon hears a footstep but does not know which side of the room it came from, then sorting molecules by that footstep is useless. The author of the paper called this useless part of the information inaccessible. The formula shows that the work depends only on the accessible information, not on all the information measured.
It is like trying to catch a fish in muddy water: no matter how hard you peer, you can see only part of the bottom. The blindfolded demon is still a demon, but its blindness is now measurable. This measure helps to assess the efficiency of real devices, where sensors are imperfect.
In the limit of infinitely precise measurement, the demon gains an infinite amount of information about the particle's position, yet it can extract only a finite amount of work, equal to kT(1+ln2). This happens because almost all of the extra information turns out to be inaccessible to the allowed protocol with a single movable wall.
In Stanisław Lem's "The Travels of Professor Tarantoga," Maxwell's demon serves as a metaphor for the limits of knowledge: even with complete information, the protagonist cannot break the laws of thermodynamics. This article shows that in the real world the constraints are even tighter: knowledge you cannot apply is thermodynamically useless.