(covers information from several alternate timelines)
The term Martian referred to anyone or anything originating on the planet Mars.
During the 20th century, when many believed that Mars was inhabited by "little green men", or other individuals otherwise described as "extraterrestrial", any "aliens" were assumed to be of Martian descent.
The War of the Worlds featured Martian invaders, whose appearance was said to have a strange horror. (ENT: "Similitude"). Incredible Tales of Scientific Wonder also featured stories about "men from Mars". (DS9: "Far Beyond the Stars")
In a deleted scene from ENT: "Storm Front", the Martians in The War of the Worlds were referred to as having inspired mass panic in the United States of America by people who feared real Martians were coming to invade Earth. In the same deleted footage, Sal admitted he sometimes wished the Martians had come.
In an alternate timeline in 1944, the Na'kuhl were described as "Martian Nazis." (ENT: "Storm Front", "Storm Front, Part II")
Similarly, during the Roswell Incident in July 1947, United States Army Air Forces Lieutenant General Denning and CaptainWainwright referred to the aliens discovered in a crashed flying saucer as "Martians". (DS9: "Little Green Men")
When Amelia Earhart was confronted with an Ocampa accompanying several Humans who encountered her in 2371, she assumed that the Humans were trying to trick her into believing Martians had invaded Earth. (VOY: "The 37's")
Following the colonization of Mars in 2103, the term was used to describe the name of the very colony placed there, aptly named the Martian colonies. (DS9: "In the Cards"; VOY: "The 37's")
The term was featured in a nonsense two-line poem that Charlie Evans forced Spock to recite in 2266: "Saturn rings around my head, down a road that's Martian red." (TOS: "Charlie X")
Spock was initially conceptualized as half-Martian, as mentioned in the draft proposal Star Trek is.... This was later changed to Vulcan instead. ("The Andorian Incident", text commentary, ENT Season 1 DVD special feature)