You probably heard the word "homozygous" in high school, but it's not a word you hear every day. Think back to Gregor Mendel, the Augustinian friar who became obsessed with why the flowers on his pea plants were different colors. Think back to recessive and dominant traits. Think back to worksheets full of Punnett squares.
So, maybe you weren't paying that much attention in freshman biology class — it's understandable. Here's a refresher:
What we learn in high school about inherited traits has to do with alleles, which are versions of a gene — a specific chunk of DNA sequence on a specific chromosome belonging to a diploid organism (that is, anybody with two full sets of chromosomes — one from each parent). We know from Mendel's experiments with pea plants that the physical manifestation of a trait like flower color has to do with the combination of alleles contributed by both parents. Some alleles are dominant, meaning, no matter what version of the gene is contributed by the other parent, that allele will be the one that's expressed in the offspring. Other alleles are recessive, which means that the only way that version of the gene will be expressed in the offspring is if both parents contribute the very same recessive version of the gene.
Which brings us to homozygous inheritance. If both parents throw the same version of a gene into the ring, their offspring will be homozygous for that trait — and whether both alleles are dominant or recessive, whatever the baby has two of is what will be expressed. If both parents contribute different alleles for a trait, the offspring is heterozygous for a gene, which often means the dominant gene is going to be the one that's expressed, though there are some exceptions to this rule.