late 14c., rebounden, "to spring, leap," also "to spring back from a force or an impact," from Old French rebondir "leap back, resound; repulse, push back," from re- "back" (see re-) + bondir "leap, bound" (see bound (v.)).
By early 15c. in the transferred or figurative sense of "fall back, recoil," as to a starting point or former state. The sporting use probably was first in tennis; in basketball it is attested from 1914. In Middle English also "return to afflict" (early 15c.). Related: Rebounded; rebounding.
mid-15c. as "a rejoinder, a reply" (a sense now archaic or obsolete); 1520s, "the return or bounding back of something after striking, act of flying back on collision with another body" in reference to a ball, from rebound (v.); rebounding in this sense is from late 14c.
In modern sports, from 1917 in ice hockey, 1920 in basketball. Transferred and figurative senses from 1560s; the meaning "period of reaction or renewed activity after disturbance" is from 1570s, hence "during a period of reaction after the end of a romantic or marital relationship" (1859).