A brown Dalmatian is a dog of the Dalmatian breed with spots which are brown instead of black. In Dalmatians, brown is called liver. Both liver and black are standard colors for the breed, although liver is less common.
Besides factors of demand and popularity, part of why liver is the less common color is due to genetics. Liver is a recessive variant of black. Both black and liver are produced by a pigment called eumelanin, the same pigment that is responsible for human variations in skin color. Dogs can carry either the black or liver copy of the gene that affects how dark eumelanin will appear in their coats. Dogs with one or two copies of the black gene will be black; only dogs with two copies of the liver gene will be brown.