Immortal children are human infants and toddlers turned into vampires. They are said to be so beautiful it takes just one look to be under their control. In addition, it is said that an immortal child's tantrum can kill people.
It does not say about whether or not the Immortal Children could gain any supernatural talents, but that they have the standard superhuman strength and speed. Because they were too young to be 'tamed', the Volturi had to hunt down and kill them all, and the people associated with them as they posed a serious threat to the exposure of the vampire world.
Creating one has become the worst crime in the vampire world, under penalty of death for both creator and created. Under this law, anyone who knows about or stands by the child is also punishable under this law.