means Evidence or reasoning sufficient to establish that something is true, or a test demonstrating quality or strength.

from From Latin 'probare,' to test or prove (also the root of 'probe' and 'probable'), which gave Old French 'prove' before settling into English. The original sense was 'a testing,' which still echoes in odd corners: the 'proof' of alcohol (a test of its strength), a 'proof' from a printer (a trial copy), and the old proverb 'the proof of the pudding is in the eating' — meaning the test of it, not the evidence.