Technically, it is the probability that two genes of a pair in an individual will be homozygous because they are replicates of a single ancestral gene. The increase in homozygosity resulting from inbreeding has several ramifications. One is an increase in the uniformity of the offspring of an inbred parent. This occurs because any pair of homozygous genes can only produce one type of gene to be transmitted to an offspring, and a set of these pairs will produce a consistent set of transmitted genes. To use the poker analogy, an inbred animal is like a deck of cards which contains just one suit.
Every deal produces a flush.
Inbreeding is commonly justified by cattle breeders as a way of increasing prepotency or breeding consistency. Increased homozygosity can also result in the surfacing of deleterious recessive genes - hence inbreeding's bad reputation for producing undesirable traits. However, inbreeding does create an opportunity for deleterious recessives to be paired in an individual, thus allowing them to be expressed. Inbreeding can, therefore, be used as a test to check for the presence of harmful recessive genes in an animal. Sire x daughter matings are an example of such a test.