Ash is what's left after something has been burned by a fire. You need to clean the ash out of a wood stove or fireplace every once in a while.
After you burn wood in a fire pit or in a bonfire on the beach, there's ash left behind. Cigarette or cigar ash is what smokers tap off the end every so often — the burned part of the cigarette becomes ash. If you use the idiomatic phrase "it turned to ashes in my mouth," you mean that something was a huge disappointment or letdown.