Here's the key statement in the article: "Important properties are actually determined by the flaws,..."
Many useful devices, like those found in computer circuits, are made from crystalline materials like silicon. The silicon atoms are arranged in a predictable, repeating pattern.
The equations describing how electons behave in a pure silicon crystal are fairly well understood, but the equations apply to a crystal that is infinite in extent.
Real crystals have edges and boundaries where the repeating pattern of the silicon crystal is interrupted. The silicon atoms in these boundary areas are not positioned exactly as they would be if they weren't near the edge of the crystal.
Electrons that get near the edges of the crystal are able to undergo changes in energy that don't occur in the interior of the crystal.
An analogy might be to consider how boats behave while floating in a lake. Every prediction about such boats would be worthless if the boats always had small leaks that permitted water to flood the boat and sink it.
The behavior of electrons at the edges of silicon crystals can be similar. The electrons can "leak" from one energy level to another in a way that cannot occur in the interior of the crystal. When electrons have leaked, they are replaced by other electrons from the interior of the crystal, and then those replacement electrons leak. The net result is a "current" of electrons that dominates the behavior of the entire crystal.
The extremely tiny flow of electrons that happens in the interior of the crystal is completely swamped by the much larger currents that exist at the edges.
The significance of the article is that an improved method for calculating crystal behavior has been developed which permits larger models of real crystals to be modelled, resulting in more accurate predictions of how real crystal devices might behave.
Thank you. Direct and clear. Do tell!