late 14c., "intercessory prayers or pleas on behalf of another," from Old French sofrage "plea, intercession" (13c.) and directly from Medieval Latin suffragium, from Latin suffragium "support, ballot, vote; right of voting; a voting tablet," from suffragari "lend support, vote for someone," conjectured to be a compound of sub "under" (see sub-) + fragor "crash, din, shouts (as of approval)," related to frangere "to break" (from PIE root *bhreg- "to break"). On another theory (Watkins, etc.) the second element is frangere itself and the notion is "use a broken piece of tile as a ballot" (compare ostracism).
The meaning "a vote for or against anything" is from 1530s. The meaning "political right to vote" in English is first found in the U.S. Constitution, 1787.