In adaptations of the novel, the Phantom's face is often portrayed as being disfigured by some kind of accident, such as a fire. This is not based on anything in Leroux's novel, but it does provide a visual explanation for the Phantom's deformity.
The Phantom's ugly face is a symbol of his inner ugliness. He is a tortured and tormented soul, who has been rejected by society. His deformity reflects his pain and suffering.
The Phantom's face is also a reminder of the dangers of vanity. The Phantom was once a handsome man, but he became vain and arrogant. This led to his downfall, and he was ultimately disfigured.