c. 1200, prēven, pruven, proven "to try by experience or by a test or standard; evaluate; demonstrate in practice," from Old French prover, pruver "show; convince; put to the test" (11c., Modern French prouver), from Latin probare "to make good; esteem, represent as good; make credible, show, demonstrate; test, inspect; judge by trial" (source also of Spanish probar, Italian probare, and English probe), from probus "worthy, good, upright, virtuous."
This is from PIE *pro-bhwo- "being in front," from *pro-, extended form of root *per- (1) "forward," hence "in front of," + root *bhu- "to be," source also of Latin fui "I have been," futurus "about to be;" Old English beon "to be;" see be.
From early 13c. as "render certain, put out of doubt," also "establish the validity or authenticity of a will, etc." By c. 1300 as "test and find worthy, virtuous, false, etc.," also "find out, discover, ascertain; prove by argument." By mid-14c. as "check the accuracy of." The meaning "be found to be (a hero, coward, etc.) by experience or trial" is by late 14c.
The word had many more senses and broader application in Middle English than Modern English: "to experience; to strive, endeavor; act, accomplish; thrive, succeed." Also in Middle English in a now-obsolete sense of "approve, sanction, praise" (c. 1300; compare approve). Related: Proved; proven; proving. Proving ground "place used for firing cannons for making ballistics tests and testing powder" is by 1837.