Mist was produced from the air's humidity when the dew point was reached and microdroplets of water or ice were suspended.
In 2267, Boma was unable to see the Taurus II anthropoids through the mist, but Spock could. (TOS: "The Galileo Seven")
In 2269, Leonard McCoy described the mists surrounding USS Enterprise as being similar to a macromorphase enzyme, warning that they'd be digested if the shields went down. (TAS: "One of Our Planets Is Missing")
Later that year, after the swoopers got sprayed with a chemical sprayer used by James T. Kirk, he believed that the creatures were waiting for the mist to clear. (TAS: "The Infinite Vulcan")
In 2367, Beverly Crusher asked USS Enterprise-D's main computer what the mist she was seeing around the starship was. The computer replied, "Sensors indicate it to be a mass energy field seven hundred and five meters in diameter". (TNG: "Remember Me")
In 2373, Korenna Mirell described the beauty of the Danius Cliffs, saying, "You'll know what beautiful truly means when you stand on the cliffs on a rainy morning and watch the raindrops turn to mist when they hit the molten sea." (VOY: "Remember")
Mist could also be a metaphorical representation of obscurity. According to Gul Dukat, "Joining the Dominion will save billions of lives and keep the Federation from fading into the mists of history." (DS9: "By Inferno's Light")