Candidate

The fact that the words "candid" and "candidate" share the same roots (the Indo European root word "kand" , that means "to shine" and is also the root for the word "candle") should not come as a surprise. What is interesting though is the reason why the word is used to refer to someone who is seeking a political position. In ancient Rome, by tradition, a person who would run for a political office would wear a white colored toga. This was more symbolic than a rule as it hinted at the purity of the person running for the political position (Ha! you would say, given how we perceive political candidates today, irrespective of our race or nation). So, though candidate is literally translated as "clothed in white", it was borrowed in English to refer to a political-position seeker, thanks to a Roman tradition.

Quarantine

Quarantine - A condition of enforced isolation.

The word comes from a Venetian custom in the Middle Ages when ships arriving from the reported plague-stricken countries were obliged to spend 40 days (Italian "quaranta" or "forty" comes from the Latin "quadraginta," also meaning 40) at the port, in isolation, before being allowed to unload its cargo and crew. Venice, in those days, was the chief European port of entry and Europe had experienced many epiemics of plague. Forty days was supposed to be long enough to kill the infection for goods (and people) by exposure to air and sunlight.
The current usage of the word is not limited to 40 days but "any period" of isolation.

Trivia: Quarantine first appeared as a legal term in 1609, as the period of 40 days in which a widow could remain in her dead husband's house before creditors could seize it.

Sources: answers.com, etymonline.com, Wikipedia