A genetic carrier is an individual who has inherited an allele for a disorder but does not display symptoms of the disorder.
The most common example of a carrier is an organism who possesses one copy of a recessive allele for a Mendelian factor. Such an individual will therefore be able to pass on the allele to the next generation without actually having the disorder. If two carriers for a recessive allele mate, then their offspring could inherit both recessive alleles and therefore contract the disorder. A very common example of such a disorder is cystic fibrosis.
The term "carrier" is usually applied in the context of genetic disorders, but it can also simply be applied to someone carrying a recessive allele for a trait.