A typical example of linebreeding would be what in human parlance would be considered a mating of first cousins or more distantly related individuals who share a common ancestor.
While linebreeding is less likely to cause problems in the first generation than does inbreeding, over time, linebreeding can reduce the genetic diversity of a population and cause problems related to a too-small genepool that may include an increased prevalence of genetic disorders and inbreeding depression.