A heterozygote is a living thing that has two different versions of a given gene. If a cat inherits a gene for black fur from its mother and one for gray fur from its father, it is a heterozygote.
The different forms of a gene are called alleles. Organisms inherit one allele for each gene from their biological parents. If those genes are different — e.g., one for gray fur, and one for black fur — the offspring is a heterozygote with respect to fur color. What color fur will a heterozygous cat have? It depends on which gene is dominant. Since the gene for black fur is dominant, the cat would be black. However, the cat could pass on the non-dominant, or recessive, gene to its offspring.