The first candidates were dressed to be noticed.
In the Roman Republic, men seeking public office wore a toga candida. Etymonline says Roman togas were usually white, but office seekers wore a brighter, gleaming one. Wikipedia says it was worn for speeches, debates and other public occasions, which is where voters could look the applicants over.
How the cloth was whitened is not settled. Etymonline says it was probably whitened with powdered chalk. World History Encyclopedia says it was bleached using sulphur, and Wikipedia says it was "chalked and bleached." Encyclopedia.com says only that it was bleached. All agree the result was whiter than an ordinary toga.
The cloth gave the word its name. Etymonline traces candidatus, "one aspiring to office," and originally "white-robed," to candidare, "to make white or bright." That comes from candidus, "shining white," and from candere, "to shine." Dictionary.com glosses candidatus as "clothed in white" and ties it to the white togas of Roman office seekers.
English borrowed the word early. Etymonline dates it to about 1600, while Dictionary.com gives 1605 to 1615. By then nobody in England campaigned in a chalked toga, so the clothing dropped out of the meaning. Only the job was left: someone put forward for a position.
Why white? Etymonline says the brighter toga was likely a signal of the purity of the candidate's intentions. World History Encyclopedia makes a similar point, saying candidates were meant to be honest and true. Neither source quotes an ancient writer for this, so treat the purity explanation as a modern guess about the custom.
The same Latin family is behind English candid. Etymonline traces the Indo-European root kand-, "to shine," to candid, candle, candor and incandescent. One word describes a person standing for election, the others describe light and plain speaking.