An allele is the singular term for a form of a gene at a certain point of a chromosome. A different form of a gene has differences in the sequence of nucleotides thus creating a different phenotype; moreover, an allele can be dominant or recessive with respect to the specific genotype.
Organisms can be haploid or diploid. Haploid organisms have one of each chromosome (and thus only one of a given allele), whereas diploid organisms have two copies of each chromosome and carry two alleles (which may be the same or different).
If the alleles are different in a diploid organism, then the organism is said to be heterozygous for that particular gene where different alleles of the same gene are present. If the alleles are the same, then the organism is said to be homozygous for the gene.
Different alleles can result in changes to the phenotype of an organism, eg. hair colour. Whether a certain allele is recessive, dominant or co-dominant can also affect expression as alleles may interact differently.