"Person of color" is essentially a tortured, PC, language construction intended to enable people to avoid saying "non-white" (which, while descriptive, is apparently insensitive or something like that).

So, for example, mixed-race President Obama is a person of color, his African father is a person of color, and his White mother is not a person of color.

It's fairly situational and the lines are relatively blurry - for example, if I have one Japanese grandparent, am I a person of color or a White person?