"Domaine" is the name given to winemakers in the Burgundy region of France. Specifically, it refers to a producer who owns their own vineyard and is involved in everything from grape cultivation to fermentation, winemaking, and bottling.
In Bordeaux, producers with the same definition are called "chateaux." While chateaux tend to be relatively large, most domaines are small-scale producers.
Another difference is that in Bordeaux, a vineyard is owned by one chateau, whereas in Burgundy a vineyard is divided and owned by several domaines.