Why do down have very good heat-insulating properties?

The quilt and the filling themselves do not keep the body warm. The feathers and down make sure that the heat of the body does not disappear, i. e. they store the heat.
 
Down are significantly lighter than feathers. With the same weight they offer a much larger volume. Due to their three-dimensional structure like a flake down are able to store large amounts of air which is not a good heat conductor. The countless air-filled buffers make up the high capacity in terms of heat insulation.
In contrast to the feather, the down is multi-dimensional. Due to its three-dimensional structure and the ability to continuously recover its original shape, a down traps large amounts of air in proportion to its weight.
 
Air is not a good heat conductor. This property works for instance with double glazed windows and cavity bricks to the effect that air forms a protective buffer from cold.
 
A good down filling contains about 2 millions of interweaved and fluffy barbs. Hence, a layer of air is formed which is a poor heat conductor and protects from cold. Due to their resiliency down can be crushed or compressed. If they are thoroughly fluffed up, they will quickly recover their old shape.
 
Quelle
Verband der Deutschen Daunen- und Federnindustrie e.V.