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Although it was obvious that Peter Parker/Spider-Man (played by Andrew Garfield) is in intense pain due to the wounds inflicted on him by the Lizard, this scene with Peter and Gwen Stacy (played by Emma Stone) is nevertheless very tender.
He'd just bravely risked his life to prove to law enforcement and the public that the Lizard was Dr. Connors, and Peter, in his alter ego as Spider-Man, was just barely able to get out of there alive. Peter feels he has no one else to turn to because Gwen is the only person he's revealed himself to.
Peter also confesses to her that it was he who gave Dr. Connors the formula for the reptilian serum - something which, in a deleted scene, the Lizard reinforces by telling Peter that, thanks to Peter, "everything changed" - and therefore Peter feels all the more motivated to defeat the Lizard.
Peter also know realizes why his late father, Richard, who once worked with Dr. Connors, kept his research on cross-species genetics a secret: because of the potentially dangerous side effects. Peter and Gwen both know, though, that defeating the Lizard won't be easy, partly because, as Gwen herself informs Peter, her police officer father has literally hundreds of other officers looking for him because they mistakenly think he's the threat.
Gwen is horrified when she sees the injuries on her boyfriend's chest, and yet, he puts on a brave smile and comforts her as they kiss. Peter bravely accepts responsibility and won't stop fighting the Lizard, despite Gwen expressing her fears for both him and her father. Also, it's only now that Gwen begins to understand not only the commitment Peter has made to saving lives, but the commitment she herself has made to him. She realizes now that if she's going to be his girlfriend - which she's already decided she will be - she has to live with and in fact sometimes face the dangers he will face.
Her tending to his injuries soon leads to the two of them swinging over the streets of New York on Spider-Man's webbings. A surprising but sweet turn from pain to romance in the Amazing Spider-Man film.