Explanation 1

Genes always sit in a specific place or "locus" on a chromosome.  Chromosomes always go round in pairs (one from dad and one from Mum) hence why we always  consider pairs of genes when looking at colours.  These chromosome loci (places) always have to be filled, but they can only be filled by one of the 3 colour genes (B,b,bl).  None of the other millions of genes that exist in the world (the cat gene pool) will fit into these loci. Imagine a child's toy only the square peg will go into a square hole.

Explanation 2

"In the beginning" all cats were "Black"  this is called the "wild type". During millions of years of evolution mutations of these genes occurred- possibly due to a zap of cosmic rays!  This produced the chocolate gene and the cinnamon gene.  If cells are examined under the microscope pigment granules can be seen -these are slightly different shapes in the 3 colours.

Mutations frequently occur in animal DNA usually the body repairs them but occasionally they get passed to offspring.  Many of these would be non-viable, for example a gene vital to the body functioning and not just effecting colour.  These non viable (fatal) mutations would be lost as offspring would not develop or would die before they could reproduce.

To be absolutely correct "In the beginning" all cats were Black based Tabbies - the self colour (solid colour) is a mutation of the tabby gene, A.  See tabby genetics later.

Explanation 3

Genes usually are inherited independently.  In this case this means that the dilute genes loci are on a different* chromosome to the loci for the basic colours gene.  Therefore when reproduction occurs the genes are not tied or linked to the coloured gene- basically imagine the genes from the parents as a number of balls, put them in a bag shake them up and pick them out one by one -this is random association. 

* slight simplification - they could be on the same chromosome but widely separated

Explanation 4

Cat hair is made up of bands of colour.   The basic colour is black on a yellowy background (the same as is seen in for example a rabbit).

The base of the hair is yellow and the tip is black.

Why does it grow like this?

There are 2 main pigments in the hair yellow (phaeomelanin) and black (eumelanin)- you may have heard of melanin -its what makes us go brown in the sun.  As the hair grows it is quite happily being filled up with black pigment, for some reason however as the hair grows a protein is produced. (this is called the agouti protein) the Agouti protein turns off the production of the black protein and therefore the lower part of the hair gets filled up with yellow pigment.  Thus each hair  has  bands and we get the ticked appearance.

The agouti protein changes the pigment production by binding with a special receptor in the cells producing the hair.  The cat has developed a very clever way to make spots and stripes.  It has reduced the number of Agouti receptors in some parts of its skin.  Therefore if there are no receptors the Agouti protein cant have an effect and  therefore the hair stays its original black colour all the way to the root.  Through evololution and then selective breeding the cat and us have developed the patterns we like the best!!  After all the effort of developing stripes and spots some breeds have been selected for the absence of pattern these are still Tabbies -they are the ticked breeds for example Abyssinian.