If an organism has two copies of the same allele, for example AA or aa, it is homozygous for that trait. If the organism has one copy of two different alleles, for example Aa, it is heterozygous.
Alleles can be dominant or recessive. A dominant allele, in combination with either another dominant allele or a recessive allele, will manifest itself outwardly in the organism. A recessive allele will only manifest itself outwardly if it is paired with another recessive allele.
For example, if the allele for white eye color is recessive, an organism will only have white eyes if it has two recessive alleles. This outward manifestation of a trait is known as a phenotype. The actual genetic configuration of alleles is known as a genotype.
So, in order for an organism to show a recessive trait, it must be homozygous for the recessive allele. In that case, there's no dominant allele there to throw its weight around in terms of phenotype.
In addition to eye color, some human phenotypes caused by being homozygous recessive for a certain gene include straight hair, attached earlobes, thin lips, congenital deafness and nearsightedness.
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