Inbreeding refers to reproduction by two organisms which are closely related.
In real-life, diploid organisms can suffer from a phenomenon known as 'inbreeding depression' where the fitness of a population lowers as it becomes more inbred. However, because of their simple genetics and haploid genetic structure, creatures are not inherently adversely affected by inbreeding - which is a good thing, as the default creatures in all games do not known who their relatives are and will happily mate with close relatives unless the hand intervenes. Some players may discourage inbreeding anyway, because they don't like it, to increase the game's challenge, or to promote genetic diversity.
There are genetic breeds for C2 and C3/DS that can recognize their relatives and will avoid inbreeding, though they may still mate with close relatives if, for example, their sex drive is pushed overwhelmingly high by agents like Cupid's Lyre.