They are indeed talking about what's left over from a fire. Ash is a
measure of the mineral content in the flour. The best way to measure it is
to burn it. The resultant ash is the leftover minerals.
The minerals vary depending on the soil the wheat was grown in. So, wheat
from Italy will have a very different ash content than stuff from Quebec,
Many professional bakers like to have flours within a certain ash range as
one gets different flavors from different ash levels.
If you're baking at home, honestly, I wouldn't worry about ash.