"structure in animals resembling a string," 1540s, alteration of cord (n.), by influence of Greek khorde "gut-string, string of a lyre, tripe," from PIE root *ghere- "gut, entrail."
Meaning "string of a musical instrument" is from 1660s (earlier this was cord). The geometry sense "straight line intersecting a curve" is from 1550s; figurative meaning "feeling, emotion" first attested 1784, from the notion of the heart or mind as a stringed instrument.