According to Khan Academy, "Challenge Patches are special awards for completing topic challenges".
Challenge patches on Khan Academy Edit
Challenge Patches are mostly found in Khan Academy's Math section. The most commonly displayed Challenge Patch seems to be the patch for Intro to JS - an hour of drawing with code. There are two identical versions of this patch, differing only in the description whether or not the challenge patch is tied to the year 2015. It is possible to have both versions, as well as the patch for drawing with code using blocks.
The most challenging Challenge Patches to obtain reach into the deep recesses of Calculus and higher mathematics study. Challenge patches are considered a specialized type of badge.