The paper for the language is here https://pgm2020.cs.aau.dk/wp-content/uploads/2020/09/tehrani... and the benefits over other PPLs are listed at a high level in the abstract.

I like the Bean Machine's declarative syntax because it makes it easy to implement interesting inference algorithms that treat different parts of a model independently. The syntax makes it easy to work around Python's lack of copyable coroutines, which e.g. has made it difficult to implement block Gibbs algorithms in Pyro. OTOH from a modeling perspective I find it easier to read monolithic straight-line models (as in STAN or Pyro) than to read declarative collections of functions (as in Bean Machine).

I second that. What's special about this language?