In the Twilight series, vampires have red eyes because they feed on human blood. Red eyes indicate that a vampire consumes human blood, which is the natural instinct for vampires in this mythology. Newborn vampires also have red eyes initially due to the presence of human blood still in their system after transformation. Over time, if vampires abstain from human blood and instead feed only on animal blood (what they call "vegetarianism"), their eyes become golden. The Cullen family is an example of vampires with golden eyes because they only consume animal blood. If vampires become hungry and haven't fed for a while, their eyes turn black. Red-eyed vampires are often portrayed as more irrational, hot-headed, and tend to travel in smaller groups compared to the more sociable golden-eyed vampires.
So, the red eye color mainly reflects diet—human blood consumption—and also the vampire's status, whether newborn or a regular feeder on humans.
