Ash is a product of fire.
When fire burns, things perish. Ash remains.
As a symbol of purification, ash is the essence that remains when all else burns away. Carl Jung speaks of such things. He says:
‘Ash’ is an inclusive term for the scoriae left over from burning, the substance that ‘remains below 
Ash, as a symbol, is closely linked to the innermost Self (Ātman). The Self, like ash, is that which “remains below.”