It depends on the context. Probably means that someone looks like they are frightened or nervous --- like the color has drained from their face, making it pale. We often say "white in the face," Example, "He was white in the face after walking through the cemetery." It could also just be a comment on the color of a person's skin, I suppose. But I don't think most native speakers would use it that way.

It can also mean someone looks unwell although we often use pale rather than white inn that context.