Homozygous refers to a situation in which an individual inherits the same alleles of a gene from both parents. The allele could be dominant or recessive. Homozygocity differs from heterozygocity because in heterozygous situations the organism has one dominant and one recessive allele instead of two of the same allele. This means that for a condition which is caused by a recessive allele, the condition will not be present in phenotype of the organism because it cannot be expressed due to the dominant allele being present. They are a carrier of the condition.
For example: Cystic Fibrosis is a condition which is characterised by thick mucus causing an obstruction in the lungs of the sufferer. Sufferers inherit the recessive allele (a mutation in the CFTR gene) for the disease from both parents. See also Albinism.