Medium used to have likes (they called them recommends). See their reasoning here from back when they replaced them with claps.
From the article:
Our system will evaluate your claps on an individual basis, assessing your evaluation of a story relative to the number of claps you typically send.
So if I understand it correctly, the idea was that claps help the algorithm learn what you specifically, as a particular reader, like the most. Think of it like a star rating system, but where instead of assigning 0 to 5 stars you can assign 0 to 50 stars to teach Medium what you like.
That was the original idea as far as I can tell. Now whether that worked out or whether it still makes sense with all the recent changes, is another question.