During the Amazing Spider-man #509 (Sins Past), Peter Parker receives a letter from Gwen Stacy from before she died. After careful examination and a confession from Mary Jane, Peter and the readers learn that Gwen had an affair with Norman Osborn seven months before she died. The result of the affair was two fully grown twins born two months premature, who were ageing rapidly due to the Goblin infected blood they had inherited from their father.
The reason Gwen was killed was because she refused to give the children to Osborn, due to the fact that she had seen what his influence had done to his own son Harry. So, it came as no surprise when it turned out Norman had taken the children anyway, and had trained the children to assassinate Spider-Man.
The decision to not simply have Peter be the father was because the editorial team felt it would age the character too much. This, of course, sparked outrage within fans, as it not only ruined the perfect character of Gwen Stacy, whom Peter constantly referred to as his moral compass (along with Uncle Ben), but also meant that Peter has two children he never discusses and does nothing about, which seemed ridiculous to long-term fans of the web-slinger.