On one level, the picture symbolizes Dorian Gray's gradual moral decay. Initially, the picture presents him as a youthful, handsome man. But over time, as Dorian descends deeper and deeper into utter debauchery, the picture comes to reflect the foul moral blackness that contaminates his soul.
The picture also represents an ideal of what art should be. According to Basil Hallward, who in some respects is Wilde's mouthpiece, an artist should create beautiful things but put nothing of his own life into them. Yet that is precisely what Dorian has inadvertently done by his whole-hearted embrace of a louche, morally-degenerate lifestyle. In painting the portrait, Basil stayed true to his aesthetic ideals. But Dorian has somehow managed to contaminate the picture with his rampant immorality.
This very much goes against the aesthetic ideals of Basil, not to mention self-declared aesthetes like Wilde himself, who maintained that there was a rigid separation between art and life and that art was a world of its own with its own values and standards. Dorian has blurred this distinction by embarking upon a life of hedonistic debauchery, and the damaging consequences of this are painfully obvious to anyone who looks at his rapidly deteriorating portrait.