  The basic idea of kin selection is simple. Imagine a gene which causes its bearer to behave altruistically towards other organisms, e.g. by sharing food with them. Organisms without the gene are  selfish—they keep all their food for themselves, and sometimes get handouts from the altruists. Clearly the altruists will be at a fitness disadvantage, so we should expect the altruistic gene to be eliminated from the population. However, suppose that altruists are discriminating in who they share food with. They do not share with just anybody, but only with their relatives. This immediately changes things. For relatives are genetically similar—they share genes with one another. So when an organism carrying the altruistic gene shares his food, there is a certain probability that the recipients of the food will also carry copies of that gene. (How probable depends on how closely related they are.) This means that the altruistic gene can in principle spread by natural selection. The gene causes an organism to behave in a way which reduces its own fitness but boosts the fitness of its  relatives—who have a greater than average chance of carrying the gene themselves. So the overall effect of the behaviour may be to increase the number of copies of the altruistic gene found in the next generation, and thus the incidence of the altruistic behaviour itself.