Krita/Manual/BrushEngines/InstantPreview
LOD strokes is Krita's special speed-up mechanism that was funded by the 2015 Kickstarter. Krita slows down with really large images due the large amount of data it's crunching in painting these images. LOD strokes works by taking a smaller version of the canvas, and drawing the feedback on there while Krita calculates the real stroke in the background. This means that if you have a 4k screen and are working on a 4k image at 100% zoom, you won't feel any speed up.
Activating LOD
LOD strokes is activated in settings of the given paintop by default. This is because LOD strokes has different limitations with different paint operations.
For example, the overlay mode in the color smudge brush will disable the ability to have LOD on the brush, so does using 'fade' sensor for size.
Similarly, the auto-spacing, fuzzy sensor in size, use of density in brush-tip and the use of texture paintops will make it more difficult to determine a stroke, and thus will slow down the brush a little.