Different skin colours,what is the science behind it?

Skin Color in Humans is an example of Polygenic Inheritance. That means more than one Gene determines what Skin Tone you will have. As I remember their are three Genes or Alleles responsible for Skin Color according to Mendelian Genetics. When the Genes from the Father and Mother come together they are expressed depending upon which Gene or Allele is more dominant.

If father has AaBaCc Genes and Mother also has AaBaCc genes the possible outcomes for skin Color can be as many as 64. However if both the parents have the same Skin Color as in the case of Americans and Europeans the resulting progeny will not be subject to any deviation form the parents skin Color.

That is both if father and mother have "aabbcc" as their genotype the resulting phenotype of the children will be the same. A cross between two True breeds yields no variation.