An allele is any one of a number of alternative forms of the same gene occupying a given locus (position) on a chromosome. An example is the gene for blossom color in many species of flower - a single gene controls the color of the petals, but there may be several different versions of the gene. One version might result in red petals, while another might result in white petals.
Some organisms are diploid - that is, they have paired homologous chromosomes in their somatic cells, and thus contain two copies of each gene. An organism in which both copies of the gene are identical - that is, have the same allele - is said to be homozygous for that gene. An organism which has two different alleles of the gene is said to be heterozygous. Often one allele is "dominant" and the other is "recessive" - the "dominant" allele will determine what trait is expressed. For example, in the case of blossom color, if the "red" allele is dominant to the "white" allele, in a heterozygous flower (with one red and one white allele), the petals will be red. The recessive allele will only be expressed in a recessive homozygote.
One exception is incomplete dominance. Another exception is "codominance", where both alleles are active and both traits are expressed; for example, both red and white petals. Codominance is also apparent in human blood types. A gene containing the codominant pure blood type alles "AA" and "BB" would result in a blood type of "AB". A third exception is "blending inheritance", present in flower blossoms as well. Codominant "blue" and "purple" alleles would result in color blending and hence, violet flower petals.