The ash content is a measure of the mineral content of the flour. A higher ash content will indicate that the flour is made from whole wheat flour, which contains more bran and germ.
The falling number is a measure of the flour's ability to absorb water and form gluten. A higher falling number indicates that the flour is more water-soluble and will produce a softer dough.
The color of the flour is important for aesthetic reasons. A whiter flour is generally preferred for cakes and pastries, while a darker flour is often used for breads and other savory dishes.