Do people know what it means when they sing it? Do they understand the words?
My view of that song is this:
You don’t have to know all the words to Auld Lang Syne, or even know exactly what they mean. Just listen to it when it’s sung and how it’s sung to know the meaning.
You can feel it.
(I know, I know. How very postmodern. I’m a cheerleader for propositional truth, no doubt. But really, we have ways of knowing and understanding that are not perfectly connected to grasping all the details intellectually.)