A recessive genotype needs to be homozygous (Both alleles the same) for the phenotype to show. The common school example of course being Eye colour of Blue or Brown. If someone is a carrier, then that means they have the allele needed for the condition, but they don't show it because they are heterozygous for it, so the dominant allele shows instead. Because only person carries the recessive allele, when they reproduce, there will be no recessive allele in the second person to connect with the recessive allele in the first person, so at best the offspring can only be a carrier too.
