When an individual has two identical genes at a locus, it is said to be homozygous (a zygote is a germ cell, e.g. an egg or sperm, and homozygous means the two have the same gene at the same locus). Individuals with different genes at a locus are heterozygous at that locus. For example, individuals that are AA are homozygous, and those that are Aa are heterozygous.
In a heterozygous locus, one of the genes might be dominant, which means that the trait it codes for will be seen and the trait coded for by the other gene (the recessive gene) will not be epxressed. For example, suppose A is dominant and a is recessive. That means whenever an organism has an A at the locus -- either AA, Aa, or aA -- the attribute coded by A is in effect. The only way the attribute coded by a is seen is if the organism is aa.