Boas' influence was also spread through his students, many of whom were to set up departments of anthropology in other universities around the country.
what does the "were to" mean?
It can mean "were going to" or "were supposed to". In this sentence it probably means "were going to". We need more information to know whether or not they did. That's what they were to do, but did they? What's next in the story?
Maybe they were to, but they didn't. Maybe they were to, and they did. I would guess that they did. In this way "were to" is used to show progression from one point in the past to another point in the past. "Would" can be used in this way as well.
It comes from "be to", which is a modal.
be to - This can be used in different ways. It can be used in place of "supposed to".
It can be used to give an order. For example, "You are to continue working on this project until it is finished." In this way, we might understand it to mean "will".
It can also mean "be going to".
We are to leave at ten AM. We are going to leave at ten AM. We are supposed to leave at ten AM.
To decide what "be to" means, one has to consider the sentence and the context.
I think "be to" has a tendency to occur more often in language that would be regarded as formal.