This is a very broad question. I would start with understanding the concept of actors. You'll end up reading about Erlang, Akka, etc.

Then what's a virtual actor and how does it differ? You'll eventually end up at the Orleans paper from MSFT research:

https://www.microsoft.com/en-us/research/publication/orleans...

It really has nothing to do with promises (as used colloquially) and is a way to design large distributed systems using message passing and localized state that's persisted.