Mutations are part of the continuous lottery of genetic recombination. The issues of recessive and dominant genes and genotypes and phenotypic genes come into play.
A mutation could be inherited from one or both 'carrier' parents. The mutated DNA will be present in all cells if only inherited from one parent, but it may not be expressed, this is what is meant by a 'carrier'.
Mutations in DNA are copied when replication of DNA takes place. So mutations may be passed on to the carrier's children, they could pass it onto theirs, and so on. Diseases of this sort include cystic fibrosis, Huntingdon's chorea and sickle cell anaemia.
Some people can carry genetic diseases without showing any symptoms at all. They carry the mutant gene alongside a normal gene, which effectively conceals the mutation. But when two such carriers have children and their mutated genes are combined, the children inherit two mutated genes and suffer the disease. This is true of cystic fibrosis and sickle cell anaemia.
Some genetic diseases are so dominant that they will cause you to suffer symptoms even if you only have one copy of the mutant gene. Sufferers of Huntingdon's chorea all appear to have one normal and one mutant gene. Scientists believe that if an embryo has inherited two mutant Huntingdon's chorea genes it is rejected by the body.
Genetic diseases persist throughout the carrier's life because the mutation affects the manufacturing process controlled by RNA. RNA transcription is otherwise very rarely faulty.