OK, but please understand that this is a widely disputed position with many subject matter experts here on MT and elsewhere holding different opinions. I will say, however, that after I came to my conclusion (detailed below) that I did some further research and also found that my new belief was echoed by a few others who are subject matter experts. While my position is in the distinct minority, I am not entirely alone.
Let's take the middle block for descriptive reasons, but the general statements and principles can be applied to all three. The middle block is typically taught as two distinct movements. First, chamber the hand/fist to the opposing hip (often with a turning or loading to that hip). I.E. sweep your right fist to your left hip, turning slightly to the left. Then explosively return to the forward facing position while sweeping the hand/fist out with the arm vertical (ish) with the hand/fist roughly somewhere below eye level. Most are apparently taught that the first movement is a "chambering" movement and the second is an outsweeping movement designed to block or parry an incoming punch, often destructively. The idea of a parry in this manner appears to have some merit but the two-part movement as a whole doesn't make sense as has been typically described. Further, it seems to always fail when pressure tested with the goal of making it perform as a two-part motion of chamber-then-parry/block. It's too slow, and no one ever seems to be able to actually chamber then bock. If they try it, they almost get to the chamber then they get punched in the face.
I contend that this is backwards. The first movement, what is commonly taught as the chambering movement is actually the block. The movement of sweeping the hand to the oposide side of the body and twisting the body is the act of parrying and using body movement for two purposes, the first of which is body movement to evade the incoming blow. The second movement, which seems to usually be taught as the block, is actually a ripost (a counter-attack after a defensive movement). It is a straight up backfist or hammer fist attack to the now parried and exposed opponent and the act of chambering during the parry adds additional power to the back/hammer fist ripost.
I came to this revelation after reading Dempsey's "Championship Fighting" in which he describes a method of fighting where the fighter keeps his guard up but leaves the fists a bit wide apart in order invite an attack down the middle (between the fists) which allows the defender to 'swat' the punch away with the palm of his hand and then immediately ripost with a backfist to the face. It's a clean, elegant, and shockingly fast two-movement set and looks almost identical, though with less "exaggerated" movements, to a classic karate high block or middle block. A low block would be the same but back/hammer-fisting low to the kidneys, short-ribs, even the groin, etc.
While I believed that this was a awesome revelation, because during years of discussions, training, and trolling the net with other martial artists, I'd never seen the suggestion before, I came to find out that it wasn't exactly a new interpretation. However, it does seem to be an, um..., "minority opinion" so to speak.
In the context of this thread, I'm not really trying to argue for or against my interpretation of traditional karate low/middle/high-blocks, but rather to illustrate that there is not really a consensus on the "true meaning and intent" of even such basic movements, never-mind something so much more sophisticated and complex as kata.
Peace favor your sword,
Kirk