A homozygote is an individual organism with two copies of the same allele that determines a specific trait, while a heterozygote has a copy of two different alleles for the same trait. Alleles are alternative forms of genes that determine the same trait.
Organisms inherit one allele from each trait from both of their parents. Typically, the terms heterozygote and homozygote are used when the traits in question are Mendelian; that is, they are determined by a single gene. Of the alleles for that gene, one is typically fully dominant over the other. A dominant allele in Mendelian genetics is always expressed over a recessive one. A heterozygote generally has one copy of both the recessive and dominant alleles for a trait, resulting in an organism that expresses the dominant trait yet can pass the recessive trait onto its offspring, according to About.com.