So what's the story behind this, I'm not really a comic reader so I'm not familiar with it.
Gwen Stacy, the girl here, was Peter's first love. She got killed in the comics decades ago when Green Goblin dropped her from a bridge. Spider-Man catches her, but the swiftness of the action ended up snapping her neck. It was a really big deal at the time because no hero had ever failed so tragically before.
This comic which came out a decade ago, retconned in a twist that Gwen was having an affair with Osborn months before she died, and that she may have even given birth to his children. And part of Osborn's motivation in killing her was really to cover up the scandal or whatever.
It's really dumb.