Vernon Dursley was a young man Petunia attended college with. She described him as fat and as the only boy who would talk to her.
At one point in their relationship Vernon told Petunia that he wanted children, and that their first son would be named Dudley. At that point, Petunia saw her whole life stretching out in front of her, and she didn't like what she saw.
Petunia and Vernon never married, and what happened to him after Petunia broke up with him is unknown.