a smaller volume of air around your body equals a smaller mass of air. it's easier for your body to heat a smaller mass of air, so it warms up faster. for example, how fast does your body heat a cold bedroom? now,...how fast does your body warm up the smaller amount of air trapped under the covers on your bed? that's pretty much the idea behind it. to put it another way, is it faster to heat half a kettle of cool tap water for tea, or a full kettle of cool tap water? with all other factors being equal, it's always easier to heat a smaller mass of anything than a larger mass of the same thing.
however, in the case of the sleeping bag, don't carry this to an unwarranted extreme. it is trapped air in the insulation and between your body and the inside of the sleeping bag which contributes to its warmth. i don't believe the bag would be as warm if all of the air trapped between your body and the inside of the bag was removed.
at this point i'll stop and let someone who understands the principles of heat transfer better than i do take over.