I'd get hit for stupid things like looking at my opponents hands, getting caught out of position, but for the most part just plain being unaware of what's happening.

To name a few here's some of the fighters who embody the essense of awareness that come to mind, Pernell Whitaker, Mike McCallum, Roy Jones, Floyd Mayweather jr. and oh yeah-- I can't leave out Wilfredo Benitez, and Nicholino Locche.

They all had the uncanny awareness of what was happening in the present, right down to as it was unfolding. They could see how their opponent was trying to counter, among many other things. On their high level of fighting they could basically steer the fight into any direction that they wanted.

I think part of it has to do with familiarity with particular situations, using your stance and punches to tone down the unpredictability or options of your opponent, but ultimately observing actions as they unfold and knowing what to do when the time comes.