The term "recessive gene" is part of the laws of Mendelian inheritance created by Gregor Mendel. Thus if the parents are closely related (in-breeding) the probability of both having inherited the same gene is increased and as a result the probability of the children showing the recessive trait is increased as well. If both parents are carriers, there is a 25% chance with each child to show the recessive trait in the phenotype. Instead, "expression" here refers to the observance of the gene within the phenotype.
Note that "expression" in this sense does not refer to genetic expression (i.e., transcription and translation) of the gene. Thus, both parents have to be carriers of a recessive trait in order for a child to express that trait. If a genetic trait is recessive, a person needs to inherit two copies of the gene for the trait to be expressed. Every person has two copies of every gene on autosomal chromosomes, one from mother and one from father. In genetics, a recessive gene is an allele that causes a phenotype (visible or detectable characteristic) that is only seen in a homozygous genotype (an organism that has two copies of the same allele) and never in a heterozygous genotype.
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