What is being carried by a genetic carrier?

A genetic carrier has a dominant and a recessive version of an allele.

Normally, the term genetic carrier is used in relation to genetic illnesses where two copies of the recessive allele cause that illness. Therefore, a carrier does not have the illness themself (as the dominant, non-disease allele is expressed over the recessive allele). However, they have the ability to create an offspring who has the double recessive genotype and therefore has the condition if they mate with another carrier or someone who is double recessive (who has the disease).