It's been awhile since I read it so you should finish the book for the "official" explanation.
Dawkins discusses a number of situations where apparently altruistic behavior can be shown to be based on conserving individduals who share genes with the altruistic individidual. The genetics of the bee hive is particularly interesting.
My concern is that he may be overstating the case. I wonder (without evidence) if genes can be preserved in a population in individuals that are not closely related but all carry a gene for behavior which preserves the population as a whole. I don't remember this being discussed. Ok, I haven't thought it through. This thread might be the place to work it a bit.