(covers information from several alternate timelines)
A scar was a visible mark of replacement of the skin following injury or illness.
Because Doctor Temec found no obvious scar tissue upon examining Captain Jonathan Archer and Lieutenant Malcolm Reed in 2152, he told General Gosis that their deformities were not the work of a surgeon. (ENT: "The Communicator")
Hugh Culber had a scar that he had chosen to keep. It originated from an incident where he was hiking along the cliffs of Cabo Rojo and fell 15 meters and puncturing his shoulder in the process. A doctor named Kashkooli rescued him, stitching Culber's puncture wound closed with fishing line. The scar was gone after he was rescued from the mycelial plane. (DIS: "The Sound of Thunder")
Kira Meru had a scar on the side of her face. Basso was ready to remove her for being "imperfect" but was stopped by Gul Dukat who healed the scar with a dermal regenerator. (DS9: "Wrongs Darker Than Death or Night")
Jadzia Dax and Benjamin Sisko remembered the time when an Argosian lieutenant threw a drink into Sisko's face. When Sisko was up to attack the Argosian, Dax stopped him with a right cross. Sisko still had a small scar from this hit as of 2369. (DS9: "Dax")
In an alternate timeline in 2374, both, Captain Kathryn Janeway and Tuvok had scars in their face. Tuvok was wounded and suffered from blindness when a chroniton torpedo exploded right in front of him and Captain Janeway's skin featured scars following third-degree burns from the fire in Deflector Control. (VOY: "Year of Hell", "Year of Hell, Part II")
In 2375, when Chakotay took The Doctor up on his suggestion that a needle and thread be used to suture his boxing wounds, The Doctor suggested Chakotay would appreciate having a manly scar over his eye. (VOY: "The Fight")