To be more specific, people's immune response killed them. The virus was especially deadly to young and middle-aged adults because their immune systems were primed to kick into a fatal, antiviral overdrive.
One of the factors that scared people most about the H1N1 flu was its severity in otherwise healthy adults. Flu viruses are usually serious. Nobody 'just' has the flu. The 1918 flu killed more people than World War I. Less deadly strains, though, usually only kill the very young or the very old. H1N1 did the opposite. Children and old people experienced relatively mild symptoms. Young to middle aged adults, on the other hand, often died of the sickness.
Doctor Fernando Polack investigated the cause of this reversal. He found that people often died due to their own body's response to the sickness, rather than the sickness itself. When a virus invades the body, the body protects itself by making antibodies, and by an overall immune response. Much of the things we associate with being sick, like coughing, and a runny nose, are the body's immune response trying to kill the invaders. Antibodies are tailored to sicknesses, and are stored in the body after the sickness passes.
Young children had not had the flu before, and so did not have antibodies. Those old enough to have survived a flu before 1957 had already been infected by a flu similar enough to H1N1 to have antibodies that worked. Middle aged people who had the flu before, but not one similar to H1N1, had antibodies that 'recognized' the flu, but could do nothing to stop it.
Those middle-aged people were most at risk. Their bodies needed to make antibodies 'from scratch' the way children did. Unlike children, however, their bodies knew something was badly wrong so their immune system kicked into overdrive. It went on the warpath, unleashing proteins that killed everything in sight, including its host body. Many people died because their immune systems destroyed their lungs in an effort to kill the invader. As yet there is no way to stop this immune response, though there may be people who are more susceptible to it than others.
Via Nature Medicine.