How did the term "foster care" or "foster parents" come about, was Foster a person?

Old English *fostrian "to supply with food, nourish, support," from fostor "food, nourishment, bringing up," from Proto-Germanic *fostra-, from extended form of PIE root *pa- "to feed."

Meaning "to bring up a child with parental care" is from c. 1200; that of "to encourage or help grow" is early 13c. of things; 1560s of feelings, ideas, etc. Old English also had the word as an adjective meaning "in the same family but not related," in fostorfæder, fostorcild, fostormodoretc. Related: Fostered; fostering.