Alleles are different forms of a gene. For example, given the gene for eye colour there would be many different colours available. People with brown eyes would have the allele of the eye colour gene coding for this.
Take a group of friends; one friend has blue eyes, one brown, one green. Each of them has the gene for eye colour, but each has a different type- a different allele of the gene.
You will inherit one allele from each of your parents for each gene type. Some may be stronger, more dominant, than others. This will eventually determine which of these is expressed.