Basic Feather Structure 

A feather has an almost tree-like structure. It has a rachis (like a tree-trunk) off of which barbs (like branches) branch off and off of which branch, in turn, tiny barbules (like twigs). In feathers, these barbules have small finger-like appendages (called barbicles) which link each barbule to the the barbules of the barb above and below it. This gives a feather it's rigid shape. The structure described here is illustrated in the line drawing further down the page.

Basic Down Structure 

A down cluster (an individual "down feather"), by comparison, has an insignificant rachis and fewer barbs than a feather. The barbules on a down cluster's barbs also have no barbicles attaching them to the other barbs and so the barbs float freely from one another, giving down it's soft feel and allowing it to trap pockets of air very efficiently for it's size and weight.