When someone talks about universals in literature, they mean those things that connect anybody anywhere to anybody else anywhere/time else. Universals are things like birth, death, gain, loss, progress, family, conflict, challenges, rising above, falling down, love, hate, courage, hope, hopelessness--they're human things. They aren't tied to or owned by a particular culture, race, gender, or generation. They just are.
Sure, universals may be expressed in different ways in the east and west, in the past and present, from language to language. But every beloved story has them--those commonalities that connect us. Granted, sometimes the reader has never considered the universal in such a way. Sometimes we need to understand the culture to interpret the universal someone is expressing, to know why they hold courage higher than most or why they refuse to allow hate into their minds or why they look at loss as beautiful when we may look at it as a tragedy. But the universal is there. The connection can still be made.
That's why universals are just short of holy. They transcend. We all know that people of the world don't always get along. We argue, blow each other up, and do all manner of ugly things to each other for something as small as money, power, or tradition. But you can't blow up the concept of love. You can't take it away from people. As intelligent as humans are, as amazing and creative and stupid--there are things we can't touch, sacred things like fear, loneliness, friendship, and hunger. Some are part of being spiritual creatures, some part of being physical creatures. Whatever the case, they are.
You can have one person who believes the world is the center of the universe, that everything in existence revolves around humans, that our story is the story; then you can have another person who believes we're just a part of a natural cycle, that there are likely many cycles like ours somewhere else in space, that our sun is just another star and our planet no more significant than any other; then you can have a person somewhere in the middle, not sure what to think about existence, not sure if she should bother thinking about it at all. They can fight all day about what to do before death and what happens after death. But all three will face that moment. Death is the constant. All three have a heartbeat, and all three hearts will stop beating. Where religion, politics, and culture break ties, the universals reconnect them.
I've heard it said that people are the same everywhere you go. No they're not. They're very different. They're all completely different. There's not two the exact same in the history of the world. But they all live and breathe and assume and decide and are capable of breaking and mending.
I reckon if the world is to ever be at peace, the universals will have something to do with it.