Brut is also used to refer to wines, particularly sparkling wines (including champagne) that are maximally dry; champagne with very little added sugar.
Traditionally, sparkling wines are fermented in the regular fashion, but then bottled with a bit of extra yeast and a dash of sugar. This causes a second fermentation in the bottle, resulting in the famous carbonation that makes sparkling wines so bubbly. This second fermentation results in the production of undesirable lees, which must be removed; this is accomplished by slowly, over the course of a year, rotating the bottle until it is up-side-down, so that the lees settle in the neck, and then freezing the neck. The cap is removed, the pressure in the bottle pushes the frozen lees out of the bottle, and it is quickly recorked. But before it is recorked, a liqueur d'expédition is added; the exact composition of this liqueur is often a secret, but it is primarily comprised of the base wine and a bit of sugar. This last bit of sugar determines how dry/sweet the wine will be; in brut or nature wines very little is added.
There are a number of more specific terms to subdivide the brut classification; brut is very dry, extra brut is even more so, and brut nature (AKA brut zéro dosage or ultra brut) has no added sugar at all. The sugar content of a brut wine should always be between 0-15 grams per liter. It is worth noting that this sugar is not added just for sweetness, but to counteract the acidity of the wine.
The word brut means 'raw' or 'crude' in French; it comes from the Latin brutus, the same root from which we get the American word 'brute'.
Sweet :: doux, sec, brut :: Dry