c. 1200, relik, "a body part or other object held in reverence or affection due to its connection with a holy person," from Old French relique, relike (11c., plural reliques), from Late Latin reliquiæ (plural) "the remains of a martyr," in classical Latin "remains, remnants," noun use of the fem. plural of reliquus "remaining, that which remains."
This is related to relinquere (perfective reliqui) "to leave behind, forsake, abandon, give up," from re- "back" (see re-) + linquere "to leave" (from PIE *linkw-, nasalized form of root *leikw- "to leave"). Old English used reliquias, directly from Latin.
The general sense of "remains, remnants, that which is left after the loss or ruin of the rest" is attested from early 14c. The meaning "something kept as a souvenir, a memento" is from c. 1600. By 1590s the word had developed its weakened sense of "anything made interesting by its association with the distant past." By 1580s as "surviving trace of some practice, idea, etc.;" hence relic of barbarism (by 1809) "survival of a (bad) old custom or condition."