(covers information from several alternate timelines)
A candle was a solid mass of wax containing a wick that provides light by burning. Many Earth candles were made from the wax of the honeybee, an insect native to that planet. The wax was actually created by reducing the material of the bees' nest, or hive, into a gelatinous form and then molding it around a wick.
Prior to the advent of mass production, the beeswax candle was a relatively valuable commodity and time consuming to create. Miss Annie tried to tempt Worf with the extravagance of beeswax candles during his time in the Deadwood holo-program. (TNG: "A Fistful of Datas")
Candles were often placed on a birthday cake in certain Human traditions. (ENT: "Silent Enemy") In 2367, there were six candles on Commander William T. Riker's blue frosted birthday cake. (TNG: "Future Imperfect")
The Bajorans used candles for their ceremonies and meditations. They also decorated their temples with candles, the Bajoran shrine on Deep Space 9's Promenade for example. (DS9: "In the Hands of the Prophets", "The Circle" et al)
Candles were used as decoration in several quarters on Deep Space 9. Benjamin Sisko used candles to create a romantic atmosphere for a dinner with Kasidy Yates in 2372. (DS9: "The Way of the Warrior")
Types of candles
According to Star Trek: Deep Space Nine shopper and archivist Penny Juday one of her tasks for the production of the series was to search the countryside for unusual glass structures and bottles. One of the items she found was actually a candleholder used upside down. She ordered three hundred of these candleholders and they were used as drinking glasses throughout the run of Deep Space Nine. (DS9 Season 1 DVD special feature "Secrets of Quark's Bar)