Inbreeding is defined as the mating of related individuals, whether they are closely or more distantly related. The inbreeding coefficient of an individual is the probability that two copies of the same gene have been inherited by an individual from a common founder (an ancestor shared by both parents) or are ‘identical by descent’ (IBD). If the individual has inherited two identical copies of the gene then they are homozygous at this gene and, in fact, the greater the degree of inbreeding the more homozygous individuals become across their entire genomes. This is the underlying reason why inbreeding is a high risk for the emergence of new genetic problems within a breed.
All individuals carry some disadvantageous mutations, which normally do not cause a problem in non-inbred individuals because they are present in the heterozygous state (one copy of the gene is normal and one is mutated, but no genetic problem is present because the normal gene is expressed). In an inbred individual there is a chance that they will inherit two identical copies of the deleterious gene version, they will be homozygous and therefore suffer the consequences of this homozygosity. The inbreeding coefficient of any individual can be predicted by the relationship between its parents (using their coancestry or kinship coefficient), so can be checked prior to making a mating.
Inbreeding arises in small, genetically isolated or closed populations, like pedigree breeds, because all members of the breed trace back to a small number of founders and over the generations they become more and more related to each other. Inbreeding thus accumulates over time and this is a natural, unavoidable, process in closed populations. Certain events such as genetic bottlenecks and selection can, however, accelerate the rate of inbreeding. Bottlenecks occur when a limited number of individuals contribute to future generations, for example, popular sires will have more offspring than other individuals and will consequently have a higher chance of contributing their genes to subsequent generations.
Selection can have a similar consequence because selected individuals are likely to come from a limited number of families. Inbreeding results in a decline in genetic diversity, both within and between individuals, due to increased homozygosity, and the rate of inbreeding (or diversity loss) in a population is proportional to the effective population size (the number of individuals making a genetic contribution to the population). If the effective population size falls below 100, then the fitness of the population will steadily decline, due to the effects of inbreeding depression (e.g. reduced fertility and increased disease susceptibility), and the population may become inviable in the long term.
This is why breeders have to start managing the rate of inbreeding to reduce the risk of these potentially deleterious events.