In theory, the warnings are supposed to cultivate an atmosphere of preparedness. If Americans are vigilant against the terrorist threat, then maybe the terrorists will be caught and their plots foiled. And repeated warnings brace Americans for the aftermath of another attack.
The problem is that the warnings don't do any of this. Because they are so vague and so frequent, and because they don't recommend any useful actions that people can take, terror threat warnings don't prevent terrorist attacks. They might force a terrorist to delay his plan temporarily, or change his target. But in general, professional security experts like me are not particularly impressed by systems that merely force the bad guys to make minor modifications in their tactics.
And the alerts don't result in a more vigilant America. It's one thing to issue a hurricane warning, and advise people to board up their windows and remain in the basement. Hurricanes are short-term events, and it's obvious when the danger is imminent and when it's over. People can do useful things in response to a hurricane warning; then there is a discrete period when their lives are markedly different, and they feel there was utility in the higher alert mode, even if nothing came of it.
It's quite another thing to tell people to be on alert, but not to alter their plans, as Americans were instructed last Christmas. A terrorist alert that instills a vague feeling of dread or panic, without giving people anything to do in response, is ineffective. Indeed, it inspires terror itself. Compare people's reactions to hurricane threats with their reactions to earthquake threats. According to scientists, California is expecting a huge earthquake sometime in the next two hundred years. Even though the magnitude of the disaster will be enormous, people just can't stay alert for two centuries. The news seems to have generated the same levels of short-term fear and long-term apathy in Californians that the terrorist warnings do. It's human nature; people simply can't be vigilant indefinitely.