Immature B cells are B cells which have not been given a specific antibody producing response yet. These immature B cells await a T helper cell to present it with an antigenic fragment to which the immature B cell will read and for plasma B cells which produce the complementary antigen, antibodies and a memory B cell which will be stored in the lymph node in case of secondary exposer.
B plasma cells are antibody producing cells. These are the cells that when an antigen enters the body and can’t be stoped by non-specific immune defences produces antibodies specifically designed to combat the antigen.
Memory B cells are B cells that when an immature B cell was exposed to the antigenic fragment instead of becoming a plasma cell became a memory cell which is stored in the lymph node awaiting the next time the same fragment is encounter. The next time the same antigenic fragment is encounter the memory B cell will produce a more rapid response, as it has memory of what type of antibody needs to be produce.