The idea of kin selection was implicit in my post on haplodiploidy but let’s make it explicit. The unit of selection is the gene, not the individual. The individual is a co-operative venture by many genes to reproduce themselves [I attempted to explain why this was and it became 4 paragraphs on the origin of DNA, so let’s just take it as a given]. There’s no reason for genes to prefer directly reproducing themselves: if you can get more copies of yourself by helping someone else’s co-operative venture than your own, that’s a better investment. Doing so is known as kin selection.
The most obvious example of this is parental investment in offspring. Offspring aren’t you, but they have your genes. For a diploid sexually reproducing organism, a given allele of yours has a 50% chance of being in your offspring via common descent (sharing an allele via coincidence doesn’t count for reasons we will get to). But a full sibling is just as related to you as your child, so raising them is just as good. The technical term for this is helpers at the nest*. It’s especially likely when raising offspring is exceptionally costly and resources (e.g. territory) are very limited, so the choice is between raising siblings or nothing, rather than raise siblings or raise your own offspring.
As you might guess from the name, helping at the nest is most common in birds, but you do see it elsewhere. Golden Lion Tamarins live in groups of 2-8, but will usually have one, with a maximum of two, breeding females. Females are unable to provide sufficiently for their offspring on their own. They’re helped out by other group members, which are likely to be their own children, siblings, or sibling’s children.
Nest-helping may be at intermediate step between the “good luck, fuckers” school of parenting (technical term: r-strategist) and eusociality. For example Carpenter Bees (carpenter is a genus, there are 500+ species within it) are usually solitary, but some build nests near each other in trypophobia-inducing pattern,. show specialization and cooperation between nesting adults (e.g. one guards all nests while others forage) , and daughters sometimes share a single nest with their mothers.
One way to help your own siblings is to raise them, like helpers at the nest do. Another is to free up parental energy by taking less for yourself. From a genetic perspective, you should stop asking for things from your parents if the energy would benefit a full sibling twice as much, or a half sibling four times as much. But from the parents perspective children are all equally valuable, so they will want to switch giving as soon as resources benefit one child more than another. This is parent offspring conflict, as explained by noted evolutionary biologist Dylan Moran at 30:00 in this lecture:
More on parent offspring conflict tomorrow.
*Note: kin selection is not necessarily the only reward for helping to raise siblings; individuals may also learn parenting skills or give themselves a leg up claiming their parents’ stuff when they die.