In class Sensei would sometimes point to a line of the Kempo Hakku "Me wa shiho o miru wa yosu - The eyes must not miss even the slightest change". He'd explain that in self defence scenarios, the eyes must 'quickly catch' all the details of a new scene or environment – drunk, rowdy or suspicious people, exits, potential weapons and other dangers etc. In training it'd also be important to 'soften' the eyes so as to also take in the surrounds and make use of peripheral vision – a point also made by Musashi in his Book of Five Rings:“In using the eyes, do so in a large and encompassing way. There is observation and there is seeing. The eye of observation is strong. The eye of seeing is weak. To see the faraway as nearby, and the nearby as faraway is essential to the martial arts. To know your opponent’s sword, yet not to “see” it at all is very important in the martial arts. You should make great effort in this.” (Miyamoto Musashi, 1645, p.67).
And if you think your awareness is pretty good, you can put it to the test:
* There also great post this topic (and the awareness test above) on KungFu4Women