Brandy, in its most common form, is a spirit made from distilled wine. Wine is boiled in a still to reduce the water content, creating a greater concentration of alcohol. In quality brandies, this alcohol will usually be then aged in oak barrels. The most well know are probably Cognac and Armagnac, from France.
Additionally, there are fruit brandies like Schnapps from Germany or Austria, made by the same process but from the fermented juice of other fruits.
Technically, there is a third type called Pomace Brandy that is made by fermenting the leftover skins, stems, and pulp after grapes have been pressed for wine. The most common of this style is Grappa.