> I have not seen any website disclose to explain what exactly these button-clicks do to help anyone?

Wild guess, you entered the world of online interactions after mailing lists. These buttons address the need of people to be "contributing". Before "+1"/"like", we had "me too". People want to feel like they're supporting views they like, and that button gives them that way, leaving space for more meaningful contributions in the actual text.

It's the same thing as a nod in a 1:1 conversation. "I'm paying attention, I'm here, I agree, continue".

That's where they help, allowing a flow of communication that suits people. Looking at the cumulative number of those... "Narcissism" comes to mind.