From The School of Biomedical Sciences Wiki
An allele is the singular of one or more different forms of a gene, at a certain point of a chromosome, that is caused by a difference in the sequence of DNA.
Organisms can be haploid or diploid, diploid organisms are most common and have two sets of chromosomes, haploid organisms have only one set of chromosomes. In diploid organisms there is one copy of the gene on each chromosome, these are alleles.
If the alleles are different then the gene is said to be heterozygous, if the alleles are the same the gene is said to be homozygous.
Different alleles can result in varied expression of characteristics in an organism, for example, hair colour. Further affecting this is whether a certain allele is recessive, dominant or co-dominant.
If a dominant allele is present then this is the allele that will be expressed, if a recessive allele is present then it will only be expressed if it is homozygous.