Phoenix ash is remnants of a Phoenix. It is able to kill Eve as evidenced by Dean when he used it to kill Eve. As Bobby puts it, "ashes of a Phoenix can burn the Mother". It's the only substance that can kill her, except by certain beings and weapons.
Dean drinks a shot of alcohol containing the ashes, thus introducing the Phoenix ashes into his blood. He then goads Eve into biting him. Eve is poisoned by the ashes and dies.
Since that is a type of dust, if someone pours that in front of a Fairy, probably they have to stop to count each grain one by one.