River told Amy that what the Doctor had whispered to her wasn't his name (as Amy believed) but was "Look into my eye."
River also explained that, when she did that, she saw the miniaturised Doctor inside the Teselecta. (That part was shown in flashback, slightly later, rather than just explained in dialogue.) To both River & Amy, that meant that the shooting was a fake & the Doctor wasn't dead. They gleefully told Rory this when he arrived to find them dancing round the garden.