I've looked into this quite a bit with my interest in possibly breeding my chow (someday .. maybe .. *L*). Her pedigree has some linebreeding in it and I've found that most of the big breeders do some linebreeding in order to "set" their lines. When you look at a certain dog and it has characteristics that make it pretty obvious it comes from a particular breeder, that's generally done with some judicious linebreeding. Hopefully those traits are GOOD ones.
Linebreeding is actually, in human comparisons, inbreeding. There are no set-in-stone definitions of linebreeding. One breeder summed it up this way: "If it works, it's linebreeding. If it doesn't, it's inbreeding". But I think most breeders consider it inbreeding when you breed half siblings, or father to daughter. Linebreedings would be a bit farther out, like uncle to niece.
All of it has its place, and done right can really emphasize a line. Regardless of what you're doing, you should really know your dog's pedigree and what you're breeding to (especially with health). I see line/inbreeding done by backyard breeder types and there's often no consideration of health in those. They simply breed what's available often in order to try to get dogs with a popular trait (in chows, creams seem to be the pet owner's color of choice and I've come across a number of breeders who are simply trying to supply creams - and ignoring other issues, like elbow and hip dysplasia and eye problems).
Melanie and the gang in Alaska