Basil is working on a portrait of Dorian Gray. The portrait captures the very beautiful young man at the height of his beauty. Lord Henry happens to come over and catch Basil painting the portrait. Basil hadn't wanted Lord Henry to see the portrait or to meet Dorian, who is innocent and unspoiled. Basil knows that Lord Henry will have a corrupting influence on the young man.
Unfortunately, Basil can't keep the two apart. Dorian and Lord Henry meet at Basil's, and Lord Henry starts a conversation about how unfortunate it is that youth and beauty are so fleeting. It seems unfortunate to him that someone as beautiful as Dorian will fade so quickly, while the portrait remains beautiful.
This raises the dissatisfaction in Dorian to such a pitch that he is willing to trade his soul for this picture to age rather than him. The portrait does begin to age while he stays young.
The portrait is significant as the catalyst that sets the plot in motion. Without the portrait, it is unlikely that Dorian and Lord Henry would have met or had a conversation about art versus human life. It is unlikely without the portrait that Dorian would have been tempted into a deal with the devil.
Further, the portrait expresses one of the moral points of the novel: the signs and disfigurement of aging are not simply a result of a body getting older but of the evils we do—they are signs of moral corruption.