How does the genetic code lead to variation?

Its all about the breeding process ...

Taking humans for example, we all carry different alleles (alleles = different copies of the same gene).

We all have 2 copies of the same genes (one from father, one from mother)

Some are these are dominant or recessive (dominant genes show over the recessive ones. You need two recessive genes for the recessive genes to show)

So for example, a woman and a man both might carry a genes for blue eyes (the recessive gene) and the gene for brown eyes (the dominant gene). To the eye, they both would Brown (dominant over the blue gene). However this might change when they have children.

When the sex cells are being made, they split in two. A copy of one gene goes in one, and a copy of the other gene goes to the other (direct 50% change of either getting a blue gene or a brown gene). Now, if the sperm cell carrying the blue gene joins with the egg carrying the blue gene, then this makes two recessive genes, and make the off-spring have blue eyes. This is an example of how variation is caused. It happens like this for a lot of things (hair colour, body build-up, etc.)

It is also to do with evolution, and natural selection. A good example of this is the giraffe story

Variation in the length of Giraffe's neck originate back thousands of years, when there was little food in the deserts where these Giraffe's lived, the only food source was that upon high Acacia trees. So the giraffes with longer necks survived as they were able to reach the food, the giraffes with longer necks bred to make off-spring with even longer necks, and the cycle goes on. This is just an example, there is many different things that this happens in

There are other ways as well, cross-pollination of plants and their genetic build up, mutations in the sex cells, etc.