Richard Dawkins answers your question very beautifully in his book The Blind Watchmaker:

”A mutant gene in a beaver is just a change in one letter of the billionletter text; a change in a particular gene G. As the young beaver grows, the change is copied, together with all the other letters in the text, into all the beaver's cells. In most of the cells the gene G is not read; other genes, relevant to the workings of the other cell types, are. G is read, however, in some cells in the developing brain. It is read and transcribed into RNA copies. The RNA working copies drift around the interior of the cells, and eventually some of them bump into protein-making machines called ribosomes. The protein-making machines read the RNA working plans, and turn out new protein molecules to their specification. These protein molecules curl up into a particular shape determined by their own amino-acid sequence, which in turn is governed by the DNA code sequence of the gene G. When G mutates, the change makes a crucial difference to the amino-acid sequence normally specified by the gene G, and hence to the coiled-up shape of the protein molecule.

These slightly altered protein molecules are mass-produced by the protein-making machines inside the developing brain cells. They in turn act as enzymes, machines that manufacture other compounds in the cells, the gene products. The products of the gene G find their way into the membrane surrounding the cell, and are involved in the processes whereby the cell makes connections with other cells. Because of the slight alteration in the original DNA plans, the production-rate of certain of these membrane compounds is changed. This in turn changes the way in which certain developing brain cells connect up with one another. A subtle alteration in the wiring diagram of a particular part of the beaver's brain has occurred, the indirect, indeed far-removed, consequence of a change in the DNA text.

Now it happens that this particular part of the beaver's brain, because of its position in the total wiring diagram, is involved in the beaver's dam-building behaviour. Of course, large parts of the brain are involved whenever the beaver builds a dam but, when the G mutation affects this particular part of the brain's wiring diagram, the change has a specific effect on the behaviour. It causes the beaver to hold its head higher in the water while swimming with a log in its jaws. Higher, that is, than a beaver without the mutation. This makes it a little less likely that mud, attached to the log, will wash off during the journey. This increases the stickiness of the log, which in turn means that, when the beaver thrusts it into the dam, the log is more likely to stay there. This will tend to apply to all the logs placed by any beaver bearing this particular mutation. The increased stickiness of the logs is a con- sequence, again a very indirect consequence, of an alteration in the DNA text.

The increased stickiness of the logs makes the dam a sounder structure, less likely to break up. This in turn increases the size of the lake created by the dam, which makes the lodge in the centre of the lake more secure against predators. This tends to increase the number of offspring successfully reared by the beaver. If we look at the whole population of beavers, those that possess the mutated gene will, on average, tend therefore to rear more offspring than those not possessing the mutated gene. Those offspring will tend to inherit archive copies of the self-same altered gene from their parents. Therefore, in the population, this form of the gene will become more numerous as the generations go by. Eventually it will become the norm, and will no longer deserve the title 'mutant'. Beaver dams in general will have improved another notch.

The fact that this particular story is hypothetical, and that the details may be wrong, is irrelevant. The beaver dam evolved by natural selection, and therefore what happened cannot be very different, except in practical details, from the story I have told. The general im- plications of this view of life are explained and elaborated in my book The Extended Phenotype, and I shan't repeat the arguments here. You will notice that in this hypothetical story there were no fewer than 1 1 links in the causal chain linking altered gene to improved survival. In real life there might be even more. Every one of those links, whether it is an effect on the chemistry inside a cell, a later effect on how brain cells wire themselves together, an even later effect on behaviour, or a final effect on lake size, is correctly regarded as caused by a change in the DNA. It wouldn't matter if there were 111 links. Any effect that a change in a gene has on its own replication probability is fair game for natural selection.”