Most likely it is the result of an event that took place when the original cell that was going to form the potato first divided. The result would be one cell that contains everything needed to produce the orange color, while the other is missing something. Since all of their descendants would get the same information, one half will be orange and the other white.

I am deliberately vague about the mechanism because there are several possible ways this might happen and I have no idea which might have occurred in your case.

Mike is quite correct, including the multiple possibilities. For one thing, such abnormalities cold result from an abnormal cell division, or a chemical or physical accident, or a viral injury, or a chimeral plant tissue in the root (the equivalent of a variegated leaf) and so on.

And those were the result of a simple, single thumbsuck. There are more where they came from, including such factors as  fairy curses and Santa's elves.