If a cigar has a white ash, it shows that there is magnasium in the soil where the tobacco was grown ...
It is also a sure fire way to tell if the Cuban cigar you are smoking is a fake. The island of Cuba lacks magnesium in its soil, and the ash will be a very dark gray to even black ... hence, the more magnesium, the whiter the ash.
This is from CA's Cigar's 101:
'According to most cigar experts, a white ash is better than a gray one. This is not merely an aesthetic issue, either. "...if the soil produces a white ash - the better soil gives a whiter ash and more taste," says Fuente. He says that certain manipulations of soil can be made through fertilization, but if too much magnesium (a key ingredient in producing white ash) is added to the mix, the ash will flake, and nobody wants a messy cigar, even if the ash is white.
Of course, ash is not something you taste or smell, but a gray ash indicates that the soil was lacking certain key nutrients, leaving the cigar with insubstantial body, or perhaps little complexity-resulting in a lesser smoke.'