The Joker threatened Rachel Dawes at Harvey Dent's fundraiser party by holding a knife to her face. After asking if she was troubled by his scars, he rhetorically asked if she wanted to know how he received them. The Joker then related the following story, either an historical anecdote, or merely a tall tale, and possibly a combination of the two:
The man who would later be known as the Joker had a young wife who was a gambler. She borrowed from loan sharks, and after being unable to repay them due to her lost money, they cut her face, resulting in disfiguring scars. Some time later, "Joker" then proceeded to place a razor blade on his cheeks and created an extension of a smile, known popularly as a Glasgow Smile or a Chelsea Grin. He informed her he did it to show her that her disfigured appearance did not bother him, and he still loved her.
Tragically, his wife could not stand this newly disfigured face, which was likely in equal approximation to her own, and left him, never to return. This incident may have built upon "the Joker's" views of the world around him, if not being the major beginning factor. Whether or not this incident or his wife as he described her were real, remains unverifiable as the Joker was prone to relating conflicting anecdote's as to his facial scars' origin.
Behind the ScenesEdit
To enhance the popularity and mystery of the Joker's characters, his creators may never wish to reveal, or create, a true backstory explaining many aspects of his origins as his criminal reinvention as the Joker, including his cheek scars. They may or may not have been inflicted in the incident(s) that didn't kill him, but "made him stranger".
Coincidentally, the Joker in The Killing Joke also had a wife (named Jeannie in that case), she also played a role in the Joker's fall into evil (in this case, due to dying in an accident relating to a baby bottle heater) and there were some hints that she may not have actually existed.