There are many factors that influence the flavor of Champagne; grape variety, vineyard, vintage, blend, pressing (first, second or third?) but one of the other ways is in the content of the liqueur d'expedition which is used to top-up the bottles after they have been disgorged and the sediment removed.
This liquid contains varying amounts of sugar syrup and some reserve wine. The amount of sugar in this mixture determines the style of the Champagne:
Extra Brut
This is an uncommon style these days, resulting in a very dry wine. The sugar content or dosage is from 0-6 grams of sugar per liter. Only Laurent-Perrier's recently introduced Ultra Brut is widely available in this style.
Brut
Most Champagnes come into this category. The sugar content is from 0-15 grams per liter. In exceptional harvests the grapes have enough natural sugar to be a "Brut" style without any dosage.
Extra-Sec
Very unusual style 12-20 grams of sugar per liter.
Sec
Very unusual 17-35 grams of sugar per liter.
Demi-Sec
This style is ideal with desserts and foie gras. Most houses do a Demi-Sec. The sugar content is between 35-50 g. per l.
Doux
This style is intensely sweet at over 50 grams of sugar per liter, and extremely rare. The early Champagnes, particularly those favored in Russia (which was a major Champagne market until the revolution in 1917!) were of this style.