How do B memory cells provide immunological memory? Do they differentiate into plasma cells?
This 2005 review in the Annual Review of Immunology entitled "Antigen-specific memory B cell development" would be a great first resource in answering your question in great detail. Briefly, memory B cells (MBC), upon re-exposure to the same antigen, very rapidly expand and differentiate into antibody-producing plasma cells (PC), with the help of memory T helper cells (Th). However, more MBC are still produced by this reaction, so that a second challenge with antigen doesn't deplete the memory population.

PC are geared towards producing gobs of antibody, and not much else. Upon stimulation with antigen, MBC will produce some cytokines to attract the Th cells that are required for costimulation and regulation, but to my understanding it is the Th cells that manage the whole response, activating effector T cells ("killer" T cells), NK cells, dendritic cells, etc., and not the MBC themselves.