Terror management theory sounds like a government doctrine on how to combat suicide bombers. It is actually, however, the name for a discipline of psychology devoted to the study of how people deal with being...well, terrified. How they cope, mentally, with the knowledge that they are mortal-- that they will eventually die, with reminders of this occurring regularly in the form of other people dying. Terror management theory asserts that mortality salience (being made to consider your own death) affects people's decision-making on an individual and group level, which makes us different from every other species on earth because we are probably the only ones who can consider the possibility of our deaths. Many non-human animals can experience fear, but that instinctual avoidance of predators isn't "death avoidance" per se. They don't want to be eaten because being chomped on sucks, and being chomped on continually until there's nothing left of you probably sucks even more. At least, they don't want to try it and find out.
Humans? We also fear being chomped on-- or shot, or stabbed, or infected, or run over, or anything else which causes pain and may end us in the process. But we also fear being ended for its own sake. The cessation of our individual lives. That's scary, regardless of whether we believe another life is going to come after it. Terrence Deacon wrote in The Symbolic Species about how symbols define language use, and our ability as a species to do that amazing trick represents the co-evolution of language and the brains who use it. In other words, symbols make us who we are-- big brained apes with the capacity to entertain counter-factuals (things that could be true, or were true, or will be true, but aren't true right this instant) and use them to communicate about things that aren't right there in front of us (a symbol being something that stands for something else). We are so attached to this ability, he said, that we effectively have made symbols of ourselves, and we fear death because it represents the end of that symbol. If we end, all of the things we stand for will end. All of the significance, all of the meaning. That's what we fear.
Which could explain why terror management theorists have found that mortality salience has a particular effect on us-- it makes us want to preserve the cultural meanings we share with others in our group at all costs. When faced with something threatening, with the fact of others dying and the reminder that we ourselves could die and will die eventually, we become more insular. Less tolerant of dissent. More suspicious of defectors and traitors. More certain that our way is the right way, and more likely to adopt a "with us or against" us policy. The biggest example most Americans have of this is the aftermath of 9/11, but any tragic event can trigger these feelings. On the plus side, we can draw together with those who sympathize both emotionally and ideologically, and provide support for each other on both fronts. Unfortunately that comes with a corresponding desire to jettison, again ideologically or even physically, those who take a different view.
As with all biases, I don't think that simply realizing the existence of one and learning about it can somehow shield you from experiencing and acting on it. But I think it helps.