Under the caste System of colonial Latin America, the term originally applied to the children resulting from the union of a European and a mestizo; that is, someone of three quarters Spanish and one quarter Amerindian ancestry. During this era a myriad of other terms (mestizo, cuarterón de indio, etc.) were in use to denote other individuals of European/Amerindian ancestry in ratios smaller or greater than that of castizos. The feminine form of the word is castiza.
It was mainly used for mixed-race people who had a slightly darker complexion than that of an unmixed Spaniard, but which were otherwise of European appearance with almost no visible admixture. Under this same caste system, the offspring of a Spaniard and a Castiza was classified as a Spaniard, thus the offspring regained his/her "purity of blood".
For some castizos whose residual quarter of Amerindian ancestry wasn't apparent at all, these were simply not categorized as castizos, and were accepted as criollos (Spaniards born in the Americas).
With the fall of the empire, the distinctions of the numerous caste terminologies (other than white, black, amerindian, mestizo, mulato and zambo) lost detail. Castizos today would simply be categorized as Whites or mestizos, depending on self-identification.
For US Latinos who yesteryear would have been classified as castizos, "Light mestizos" or "euro-mestizos" are relatively common contemporary American English terms used, but more common in use is "light skinned Mexican" or other nationality.