What is the difference between an allele and a gene?

A gene is a section of DNA coding for a specific protein. This protein will perform a certain function within the organism. You interit two forms of each gene, one from each parent. These are known as the alleles. The two alleles you inherit can be the same, or slightly different, giving rise to slighty different protein products. An example of this, are the blue and brown alleles determining eye colour. Both are the same gene; they code for the colour of the iris. However, depending on your combination of alleles the actual colour of your eyes can vary.