The two genes that are paired are referred to as alleles. However, just because they exist in pairs, doesn't mean the pairs are identical. Often, they are not. If the paired genes are identical, the individual is referred to as being homozygous. If the paired genes are not identical, the term used is heterozygous.
Homozygous individuals have only one allele to pass on to their offspring.
Heterozygous individuals can pass on either of the two different alleles in their genetic makeup. This passing of traits occurs at the moment of conception. When the sperm fertilizes the egg, the paired chromosomes of each parent split, with a single set of 32 chromosomes from each joining to form a new pair for a total of 64 individual chromosomes. This means, of course, that there is a new pairing of genes or alleles. So now the potential offspring of the two individuals is endowed with a complete set of genes from each parent.