It sounds intellectual enough to invest the speaker with instant thermal authority. It's the amount of surface that can lose heat compared to the internal mass that holds and, in animals, generates heat. Car and home heat redistributors are built to have long thin shapes so their high surface area to mass ratio gives off, or radiates, lots of heat. Imaginatively, they are called radiators. Spaghetti cools rapidly.
Baked potatoes stay hot.
Like spaghetti, your fingers and ears are relatively long and thin with much exposed surface. Fingers and ears chill faster than your torso. Your torso, very much like a potato, has relatively high internal mass compared to its outer surface of skin giving it a lower surface area to mass ratio. Even though fingers have less total surface than your body they have a higher ratio, and more capacity to radiate heat. The ratio is not the main determinant of chilling, it is much less important underwater than above, and it is only one star in a constellation of temperature regulating mechanisms.