The Kazon are loosely organized into an assortment of rival clans, each perpetually trying to gain influence over the others and expand its territory. Each clan has its own leadership and hierarchy. One thing that seems common to all is a bully-like infighting, leading to rights of passage involving attacking and harming others.
A Kazon prison is a line drawn on the floor that the prisoner is told not to cross.
Kazon are red-skinned humanoids with rather pronounced bone structures in their faces, and... as if you couldn't guess... ridges in the middle of their foreheads. Kazon are typically tall and heavily built, although this may simply reflect the preferences of their military recruiters, as few (if any) civilian Kazon were ever seen. Training (or what passes as such among the Kazon) begins at a young age. They have demonstrated very misogynist attitudes on multiple occasions, and females are typically on the bottom tier of their society.
The Kazon have demonstrated little creativity in technological, tactical, or strategic matters. All of their technology is stolen, and perpetual infighting limits their organization and expansion. Their only real organizational achievement is their rebellion and overthrow of the Trabe, effectively taking over their area of influence in that region of the Delta Quadrant. The only times the Kazon have been united over anything are in hatred of the Trabe and in wanting to capture the Voyager.
Their only noteworthy technological achievement is that the largest Kazon warships are several kilometers in length. However, since all of their ships, like rest of the technology, are just stolen from other civilizations (especially the Trabe), that is only a minor accomplishment. Despite the size of their vessels, their combat capabilities are poor, requiring several of their largest vessels to even be a match for a light Federation starship (they still required inside information to have a chance).
Given their inability to function as a coherent civilization, it is likely that they will squander whatever influence they have in the coming years and be displaced by other factions.
The Kazon are a negligible threat to any well-organized government that possesses typical technology for Star Trek (phasers, warp drive, shields, etc.). The Borg consider them so pathetic that assimilating them would actually degrade the Collective.