Fix some point p on the Riemann sphere. Each Jordan curve not passing through p divides the Riemann sphere into two pieces, and we call the piece containing p the "exterior" of the curve, and the other piece its "interior".
To fix a point p on the Riemann sphere, each Jordan curve that doesn't pass through p will divide the sphere into two parts. The part containing p is called the "exterior", while the other part is called the "interior".