Ancient Roman candidates for office would put on white togas, as a form of purity and honesty signalling, and to stand out better in the crowd.
The garment was called the toga candida, from Latin candidus, 'dressed in white', and from this they were called candidati, 'ones dressed in white', which has come down more or less unchanged to Modern English, although the meaning was widened slightly.
This is well attested, for example an early etymologist Sextus Pompeius Festus writing in the 2nd century CE has this to say
Candidati dicebantur, quod togam candidam induebant.
"They were called candidates because they put on a white toga."
De Verborum Significatu, "On the meaning of words"
These white togas appear to have been whitened using chalk powder (you can still using whiting to restore your canvas plimsolls to a brilliant white).
The Latin root of candidati was candere, "to shine", which comes from an ancient PIE root *kand- with the same meaning. Other words descended for this root are candid, candle, and incendiary, as well as incense, candelabra and chandelier.