Roughly, the sets of computational problems that people used (use?) MPI for. Things like numerical solvers for sparse matrices that are so big that you need to split them across your entire cluster. These still require a lot of node-to-node communication, and on top of it, the pattern is dependent on each problem (so easy solutions like map-reduce are effectively out). See eg https://www.open-mpi.org/, and https://courses.csail.mit.edu/18.337/2005/book/Lecture_08-Do... for the prototypical use case.
