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.
Many organisms are diploid - that is, they have two sets of 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. An exception is "codominance", where both alleles are active - a blending of traits may result, e.g. pink petals.