A son; -- used in compound names, to indicate paternity, esp. of the illegitimate sons of kings and princes of the blood; as, Fitzroy, the son of the king; Fitzclarence, the son of the duke of Clarence.
Fitz is the Norman French equivalent of "son of", having the same root as French "fils" and Latin "filius". The patronymic would change from generation to generation. Then came a soldification into a surname on the order of Johnson, Anderson. Some examples are FitzAlan, FitzGerald.
(Norman french) "son of" as in Fitz William. See Early England