I think what everyone’s worried about is a mutated form of the virus that is easily transmissible from human to human. People have already gotten sick and died after catching the virus from birds. The problem is that these viruses are constantly mutating and exchanging genetic material, so a virus that kills chickens this month may become a virus that kills humans next month. With the close proximity of pigs, chickens, ducks, and humans on many Asian farms, that is supposed to be a common place for viruses to jump species.
Basically, what would have to happen is one person would have to be infected with both the deadly-but-not-transmissible version of the flu and the highly-contagious-but-not-very-serious version of the flu at the same time. If both types are present in the same cell, then because of the way the virus’ genome is organized, it can swap genetic information, and potentially create a highly contagious and deadly version. After that, of course, it would have to be transmitted to other people.
Incidentally, you could also get a rearranged not very serious and not very contagious version, but we’re OK with that.