[snikolov]

It sort of comes down to the question of what's really being learned here?

That's a great question. We are learning to recognize trends and non-trends based on previous examples. Since the Twitter trends algorithm gives us such examples, you could say we are learning to replicate the outputs of an arbitrary algorithm --- and you'd be right. But learning from examples is a very general thing, so the method has applications beyond detecting trending topics.

Are they modeling some inherent process of topics becoming popular

No, we don't model the process of something becoming popular. (To do this, one might suppose people spread popular topics in X way and unpopular topics in Y way, and try to estimate from the data whether the topic is popular or unpopular.) The beauty of this is that we never have to build a model, because we rely directly on the data. As a corollary, this approach is applicable out of the box for any domain with time-varying data (though I suppose you might have to take care to measure the right kind of time varying data).

Does that answer your question?

[Nogwater]

I think that answers it. Thanks. :)