In this sense, currents of thought would refer to the ideas currently popular in intellectual communities.
At first I wanted to think of this metaphorically. A current is a flow or rhythm; a current of thought is a tendency for thought to move a certain way in literate discourse. Fortunately Collins Dictionary has a definition of current that uses current of thought as an example.
- A particular current is a particular feeling, idea, or quality that exists within a group of people.
"Each party represents a distinct current of thought."
Currents of thought are similar to the state of the art, the current paradigm, or the prevailing theories of the day. These currents are often external to one's own subject area. Two examples from academic texts:
Some psychologists, reflecting more modern currents of thought, disagreed with Wundt's version of psychology and proposed their own. (One set of ideas influenced psychologists to reconsider their assumptions.)
Keen to respond to modern currents of thought, (reconstructionism) also implemented gender equality far more quickly than other movements. (A religious reform movement responds to contemporary discourse on gender equality by implementing it.)
Basically, if I were to open up a periodical that has some kind of intellectual bent, like The Atlantic, what sort of ideas would be under discussion? If I met another generally educated person at a party, what ideas could I presume that person to be at least a little familiar with? The idea of multiple learning styles (visual, aural, kinaesthic) aiding learning, the idea of work-life balance being important to the modern worker, the idea that the Bechdel test is a useful measure of female characters' participation in films - those ideas could be part of the prevailing currents of thought.