Thinking about it, there are probably at least three reasons why a female cat looks after the kittens of another female. We see this on the Internet quite often.
The first reason is that it could be accidental that one female cat looks after the kittens of another female cat. It may be because of a female cat’s inability to distinguish her own kittens from others. Perhaps they follow a simple method to look after all the kittens that happen to be in her nest. Perhaps she sees no need to check whether they are her kittens or not by sniffing them.
If one cat does another cat a favor then it is reciprocated. For example a female (a queen) who is to give birth in weeks might assist another female with kittens in the expectation that the favor will be returned when her kittens are born. This is beneficial to both cats. This of course can take place between any two animals who live near each other. It doesn’t matter whether they are related or not. However when they are related there is a further advantage.
If two female cats are related e.g. sisters and they share parenting of their kittens, their kittens, even if fathered by different male cats, share a quarter of their genes with their aunt. When these kittens go on to have offspring of their own each of those kittens share genes with both their mother and their aunt.
These kittens carry genes which favor cooperation between cats that are related which means they are more likely to flourish as opposed to having the genes of rival cats which promote antagonism. There is therefore a potential future advantage to the family. Neither sister knows which of their offspring is going to survive but where there is this advantage they should try to raise both litters.
P.S. This is a tricky subject. I welcome the input of others in comments which add to the page. Good comments will be added to the body of the article.