'Concede' is Latin for 'yield altogether' — from 'cedere' (to go). Giving way completely.
To admit or acknowledge something reluctantly; to yield or surrender a right, position, or point in a dispute.
From Latin 'concēdere' (to go away, withdraw, yield, grant, allow), composed of 'con-' (with, altogether — here functioning as an intensifier meaning 'completely') + 'cēdere' (to go, to move, to yield, to withdraw), from PIE *ḱed- (to go, to walk, to yield). The Latin sense of 'yielding completely' or 'going along with' someone's claim evolved into the modern sense of reluctantly acknowledging a truth or giving up a contested position. Latin 'cēdere' is one of the most prolific verb roots in English
In elections, the 'concession speech' — when a losing candidate publicly acknowledges defeat — has no legal significance whatsoever. A candidate's refusal to concede does not affect the result. The word's power in this context is purely rhetorical and social: to 'concede' is to yield publicly, and the refusal to do so is perceived as a refusal to accept reality rather than as a legal challenge.