A camera setting (automatic or manual) that adjusts colours in a photo so that white objects actually look white under the light present at the time.
Different light sources have different colour temperatures; white balance compensates for this by shifting the colour cast of the whole image. An incorrect or automatic white-balance decision can shift every colour in a photo, including eye colour.
A colour looking different in two photos doesn't necessarily mean the real-world colour changed — it may simply reflect two different white-balance decisions made by the camera.
The same pair of eyes can photograph as more blue under one white-balance setting and more grey under another, without anything about the eyes themselves changing.
Explains why eye-colour photos (and colour photography generally) are not a reliable, definitive record of exact colour.