What is the difference between a recessive and dominant allele?

Alleles are different versions of a gene. Every person has two alleles for each gene (one from either parent). For example, the gene which determines eye colour can either have an allele for brown eyes or an allele for blue eyes, an individual can have two alleles of each or one of both.

Alleles can either be classed as Dominant or recessive. If an allele is dominant its characteristics will always be expressed, even if the individual only has one copy. For example, the allele for brown eyes is dominant, so a person with one copy of two copies will always have brown eyes. 

If an allele is recessive its characteristic will only be expressed if an individual inherits both recessive alleles, or lacks a dominant allele. For example, a person will only have blue eyes if they inherit two copies of the same allele needed for blue eyes.