Genes are the basis of the idea of inheritance, what is passed down from generation to generation and more importantly genes help us understand the mechanism of this inheritance. However it was not clearly understood why some traits were inherited and others were not, why there seemed to be some sort of selection process determining which inherited traits were revealed. It is now understood that alleles, the alternate versions of the same genes, are what determine traits. It is clear that alleles can be dominant or recessive and the pairing up of either of these two alleles, homozygous (double recessive or double dominant) or heterozygous (one recessive, one dominant) directly relates to the expression of traits or why some traits are not expressed.
The fact that some traits may not be expressed in an individual is where the idea of the genotype of an individual comes in. It is the genotype that tells the whole story of a person's genetic make up, what genes they have despite if the alleles are expressed or not, if they are noticeable or not. The genotype is the genetic compliment of all the alleles. It is essential in determining the mechanism of inheritance and more significantly how recessive traits, harmless or harmful, can suddenly be expressed in the next generation. .
If the genotype of an individual is homozygous dominant or heterozygous for any given gene, it is the dominant gene that is expressed in either situation. So, even though the genotype may differ the same trait may be expressed. This expression is the phenotype of an individual, the result of the genotype. However although the genotype directly affects an individual's phenotype so does the environment they are exposed to. Thus the phenotype would seem more personal to an individual than their genotype, which includes non-expressed traits, which a person may even find irrelevant to them e.g. if they are merely a carrier to a harmful trait.