by 1781, an alteration (by influence of words in quadr-) of quarteroon (1707), "offspring of a white and a mulatto," from Spanish cuarteron (used chiefly of the offspring of a European and a mestizo), literally "one who has a fourth" (Negro blood), from cuarto "fourth," from Latin quartus "the fourth, fourth part," which is related to quattuor "four" (from PIE root *kwetwer- "four").
So called because he or she has one quarter African blood. There also was some use in 19c. of quintroon (from Spanish quinteron) "one who is fifth in descent from a Negro; one who has one-sixteenth Negro blood." OED lists quarter-caste as an Australian and New Zealand term for a person whose ancestry is one-quarter Aboriginal or Maori and 3/4 white (1948).