The concept behind a most definite 'look' in martial arts, at least Japanese ones, is that of using metsuke to promote seme. It is in essence 'striking with the eyes' to put pressure upon the opponent.
Sudden snaps of the neck are an exaggeration of this feeling. The pressure comes from the spirit of the swordsman {speaking in the art of my experience of course} rather than the physicality of the 'look'.
This sounds like nonsense but all martial arts are a game of inches and milliseconds. If you can give an opponent a fraction of a second pause or, conversely, make him 'rush' then you have gained an advantage that you can exploit.
The mantra I have heard from Kendoka on this is:
ichigan-nisoku-santan-shiriki
Roughly speaking: Eyes first; footwork second; spirit third; and power last
EDIT: Did a bit of digging on that aphorism and found this useful treatise: http://www.standrewskendo.co.uk/articles/what-is-seme-ashi/
Brilliant post!
I'd like to add to it, if I may. When I was researching my book, I read a lot of material about Gigo Funakoshi, Gichin Funakoski's son. This man was instrumental in turning Okinawan karate into a Japanese product (which was later shipped to Korea).
Gigo studied kendo and was impressed with the zen austerity of the two person kata and he wanted to create something like that in karate in order to attract more Japanese. Therefore, he ended up changing the way that karate was taught in Japan by changing the practice of basics, the performance of the kata, and by inventing the concept of ippon kumite.
This was an integral part of making karate into a Japanese art. I am willing to suspect that if we examine the history of these head turns and talk to Japanese instructors, they will give this exact explanation.
There are a lot of similarities between Japanese swordsmanship and karate. It is difficult to differentiate the origin of these influences because Shuri and Tomari systems of karate draw many technical aspects from the Jigen Ryu school of kenjutsu. From my research into the matter, it seems that these can be teased by apart by noticing the similarities between Jigen Ryu's physical techniques and actual kata application. Gigo Funakoshi's influence, and the influence of kendo, can be found in some of the more metaphysical explanations and teaching methods.