At the beginning of Chapter Six, the reader learns why Dorian Gray is so fascinated by his past and the years gone by:

"And so the years passed. But time did not touch the face of Dorian Gray...He became more and more in love with the beauty of his face, more and more interested in the ugliness of his soul."

After making his supernatural pact in Chapter Two, Dorian's beauty can never fade. In fact, no matter what he does, his beauty and youth remain unaltered. As such, Dorian is able to do anything and behave in any manner without fear of physical change. Throughout Chapter Six, the reader learns of the many scandals and secrets which surround Dorian's private life. But, looking at his face, the people of London cannot believe that he could commit such acts, and they still flock to his house, where he holds the best dinner parties in London. 

But the portrait holds all of Dorian's secrets: 

"The terrible face showed the dark secrets of his life. The heavy mouth, the yellow skin, the cruel eyes - these told the real story."

As such, Dorian develops an obsession with looking at the painting. Initially, he enjoys looking at it and he laughs as its becomes uglier and more aged. But, as the years pass, his compulsion creates a strong sense of fear. He is terrified that someone will discover the truth and, as such, he cannot bear to be parted from it:

"Sometimes, when he was staying in friends' houses, he suddenly left and hurried back to London. He wanted to be sure that the room was still locked and the picture was still safe."

So, for Dorian, his interest in the years that have passed is inextricably linked to his feelings about the portrait. While at first he relishes in his inability to age, he soon becomes terrified of his true nature being revealed to the world. This fear also serves to drive the book's plot: it leads directly to Basil's murder and will eventually be the cause of Dorian's own demise.