Basically, in places where you can't find dry tinder easily, shaving a stick of wood until you have fine feathery shavings will allow you to create the conditions for a fire to catch and grow. Mors Kochanski showed us how he was able to ignite a feather stick using a ferrocerium rod which we all thought was fairly impressive... You could use a flint and steel to make an ember, or a fire piston, or a good ol' fashioned match.
Making feather sticks tests your knife craft skills. Mors Kochanski writes in Northern Bushcraft that you must create the shavings on one plane of the stick. He isn't saying you need to be precise in keeping the curls all facing the exact same direction, but rather that you shouldn't be creating feathers all away around the circumference of the stick. Using my Mora, I use the curved part of the blade at the front, this helps curl the strips.
The video below shows how you can feather a stick of wood to make fire in damp weather.
Woodcraft Wanderings has a very detailed and informative article that illustrates the making of fire using feathersticks and many other types of tinder.
Ben of Ben's Backwoods fame has a good article on feather sticks. It demonstrates good technique, and finishes with the note "The key is observation, practice and a sharp knife. Be patient and keep trying."
I would agree.
Cheers,
Mungo