Dominant alleles show their effect even if the individual only has one copy of the allele (also known as being heterozygous?). For example, the allele for brown eyes is dominant, therefore you only need one copy of the 'brown eye' allele to have brown eyes (although, with two copies you will still have brown eyes).
If both alleles are dominant, it is called codominance?. The resulting characteristic is due to both alleles being expressed equally. An example of this is the blood group AB which is the result of codominance of the A and B dominant alleles.
Recessive alleles only show their effect if the individual has two copies of the allele (also known as being homozygous?). For example, the allele for blue eyes is recessive, therefore to have blue eyes you need to have two copies of the 'blue eye' allele.