(covers information from several alternate timelines)
Spock draws a "mystic symbol"
While standing in the symbol he uses his magic powers to move a chess piece
Sulu conjures a woman
Magic was an art which proposed to make use of the supernatural to control or overcome natural events. One who made use of magic was known as a magician. Some races, such as the Megans or the Q appeared to use magic. Some religious groups also claimed to use magic, such as witches. (TAS: "The Magicks of Megas-Tu") Other terms for a magician were sorcerer and wizard. (TOS: "The Deadly Years")
As a child, Gary Mitchell was interested in magic tricks, which along with his skill at guessing games, foretold his extrasensory abilities. (TOS: "Where No Man Has Gone Before")
In 2367, the impostor styling herself as Ardra used a number of tricks that some described as magic. When she used one of these to appear as a Starfleet ensign, Commander William T. Riker told her that he wasn't impressed by her magic tricks, but she replied that she pitied him, for "We live in a universe of magic, which evidently you cannot see." Later, when Captain Jean-Luc Picard revealed the truth about her magic, Picard stated "Ardra controls her magic literally by the blink of an eye, centuries old technology – an implant that allows her eye movements to choose and activate each illusion." (TNG: "Devil's Due")
In 2376, when the Fair Haven holoprogram (Paris 042) began malfunctioning such that the characters began noticing the USS Voyager crew's interactions with the program, a number of the characters in the program began to blame these occurrences on "unholy magic." (VOY: "Spirit Folk")
Magic in the universe of Megas-Tu
In the alternate universe in which Megas-Tu was located, magic was the natural law. The Megans used magic in their daily lives. When the USS Enterprise was accidentally transported to this universe through the creation point in the galactic core, they found that they could use magic abilities that did not exist in the "normal" universe. Spock explored these new abilities by drawing a mystic symbol on the floor, and while standing in it, used the power of his belief to move a Vulcan chess piece. Sulu used magic to conjure up a beautiful woman before Lucien warned him that using mental powers would attract unwanted attention. (TAS: "The Magicks of Megas-Tu")