Dominant alleles are always expressed in the organism, while recessive traits tend to be expressed only when the dominant allele is not present. The relationship between dominant and recessive genes is described by the Law of Segregation. As related by About.com, Gregor Mendel observed nine different traits among his pea plants and found that certain traits, such as pod color, bred true only when two recessive alleles were present.
Sexually reproducing organisms carry two copies of each gene in their DNA. When these two copies are the same, or "homozygous," their effect is to produce whatever trait the genes are identified with. When different versions of the gene are paired, however, what usually happens is that one gene is expressed at the expense of the other. The expressed trait is then described as dominant.
By carefully isolating nine separate traits in his pea plants, Mendel was able to show that each trait--such as plant height and pod color--bred true in self-fertilized plants. When the plants were cross-fertilized, however, their traits did not blend; tall and short plants didn't produce medium-height plants, for example. Instead, according to Genome.gov, three out of four offspring were tall. In this case, tall was a dominant allele.