The Black Cat, created by Al Gabriele, was among the first comic book superheroines, appearing in the first issue of Harvey Comics' Pocket Comics, August, 1941, four months before DC/National released Wonder Woman. We cannot really call her the first, however, since Phantom Lady appeared in Quality Comics and Miss Victory in Holyoke Comics during the same month.
Her secret identity was Linda Turner, a Hollywood actress who had started her career as a stunt woman, thus explaining her above-average physical abilities. Although characters such as Superman were proving popular, many heroes of comicdom's Golden Age had no super powers; they were merely talented people with a thirst for justice and a fetish for bizarre outfits. In Linda's case, she put on the disguise and skimpy costume to track down a director whom she had learned was a foreign spy. She knew him to be highly superstitious, and believed the black cat theme would, (to paraphrase the Batman) strike terror into his heart.
Linda enjoyed the experience, and continued to fight crime, transferring to Harvey's Speed Comics and, in 1946, to her own title. Superhero titles, however, were in decline after the war. She was briefly given a young sidekick, the Black Kitten, but Harvey dropped her as a hero in 1951. The comic continued as Black Cat Mystery, a mystery and horror anthology series. Several attempts have been made to revive her, but the character has never caught on again.
Her biggest legacy may be the similarly-clad Black Canary, a knock-off created by DC (think The Cat and the Canary. In all fairness, the DC heroine has a more interesting origin) who has outlasted her inspiration and continues to battle crime. Both characters inspired Marvel's Black Widow.
Some of the information in this node came from Don Markstein's Toonopedia.