The coat pattern in Siamese cats is a form of partial albinism, resulting from a mutation in tyrosinase, an enzyme involved in melanin production. The mutated enzyme is heat-sensitive; it fails to work at normal body temperatures, but becomes active in cooler areas of the skin. This results in dark colouration in the coolest parts of the cat's body, including the extremities and the face, which is cooled by the passage of air through the sinuses.
Many early Siamese were cross-eyed to compensate for the abnormal uncrossed wiring of the optic chiasm, which is produced by the same albino allele that produces coloured points. However the crossed eyes have been seen as a fault and through selective breeding, the trait is far less common today.
Details of the Tyrosinase mutation are available in this 2006 paper: Albinism in the domestic cat (Felis catus) is associated with a tyrosinase (TYR) mutation