Explain the concept of recessive and dominant alleles

Firstly it is always good to relate such a concept with an example that is easily remembered and therefore easily applied. Alleles refer to alternate forms of the same gene, which code for a particular trait such as hair colour, or eye colour. A good example of a recessive allele is the one for blond hair; its dominant allele is brown hair. In this case the gene we are concerned about is the gene that determines hair colour, and the different forms of this gene, the alleles, will determine the colour of the hair that grows on a persons head.
The allele for blond hair is referred to as 'b', and the allele for brown hair is referred to as 'B'. The allele for brown hair is dominant which means that if present in a genes (genotype), it will automatically be expressed as a trait (phenotype). The blond phenotype will only be expressed if both the alleles are the recessive blond 'bb', this is called homozygous recessive. 
A Punnett grid can be used to show how recessive alleles are passed on.
From the Punnet grid the genotypes can be deduced using the concept of recessive and dominant alleles.
BB = brown
Bb = brown (since 'b' is recessive and will therefore not have an effect on the phenotype) 
bb = blond (since there are no dominant alleles, and it is homozygous recessive, the phenotype will be blond).