In 1877, Giovanni Schiaparelli, an Italian astronomer, put forth that Mars was covered in a network of lines, which he called "canali." One translation of this was "channels," but it was translated the other way, as "canals." And thus was the legend of Martian canals was born.
Some scientists, the chief one being Percival Lowell (discoverer of Pluto), thought that the "canals" were for irrigation and that it proved there was life on Mars. By 1909, however, a majority of scientists had realized the mistake -- the "canals" were merely an optical illusion and Mars was much too cold and dry to support water or life.
That didn't stop the public going crazy for them, however. Books about Mars became the rage: Edison's Conquest of Mars by Garrett P Serviss had the Wizard of Menlo Park conquer the Martians after their botched invasion in War of the Worlds; Edgar Rice Burrough's wrote A Princess of Mars, which became wildly popular; C. S. Lewis wrote Out of the Silent Planet and Ray Bradbury wrote The Martian Chronicles. All of these stories feature Martian canals.
Some people even reported contact with "Martians." Carl Jung's 1902 doctoral dissertation describes a "young Swiss woman who was agitated to discover, sitting across from her on the train, a 'star-dweller' from Mars. Martians are innocent of science, philosophy, and souls, she was told, but have advanced technology. 'Flying machines have long been in existence on Mars; the whole of Mars is covered in canals,' and so on." (Carl Sagan, The Demon-Haunted World, page 111).
In 1971, Mariner 9 orbited Mars and transmitted clear images of its surface, finally completely killing the idea that Mars ever had canals.
(Source: Carl Sagan, The Demon-Haunted World, Martian canal Wikipedia page.)
(Image source: Wikipedia.)