Line breeding is a type of inbreeding where the influence of one individual is emphasized. This is done by breeding to dogs that go back in a straight line to that individual. That way the influence of a great individual can be brought forward and concentrated in a present litter. Family breeding is a type of inbreeding where the influence of a group of related individuals can be concentrated in a present litter. These related individuals can be any combination of littermates, parents, grandparents, aunts, uncles, nephews, nieces, cousins, etc.
As family breeding progresses, the breeder will often line breed to an exceptionally outstanding individual that has appeared within the family. This can continue until line breeding to that individual is no longer productive. At that point the breeder can continue the family by breeding to the best individuals available within the family until the next outstanding family bred individual appears. Then, once again, the breeder can move the family forward by another round of line breeding to that individual.
One advantage of family breeding over traditional line breeding is that there is a wider variety of individuals from which to select since the breeder is not limited to the occasional outstanding individual worthy of inbreeding. This broader genetic base enables the family to be continued into the future. Also, family bred dogs are less likely to carry recessive defects since they are more likely to have already surfaced and been culled from the family. As with all forms of inbreeding, judicious selection and culling is essential for success with either traditional line breeding or family breeding.
Keep in mind that no matter how close or how long you line breed or family breed, no defects are created nor are any good traits created. Any form of inbreeding merely gives both good and bad characteristics a better chance to appear and perhaps show up in a more concentrated or extreme form.