All of the plasma cells descended from a single B cell produce the same antibody which is directed against the antigen that stimulated it to mature. The same principle holds with memory B cells. Thus, all of the plasma cells and memory cells "remember" the stimulus that led to their formation.
The B cell, or B lymphocyte, is thus an immunologically important cell. It is not thymus-dependent, has a short lifespan, and is responsible for the production of immunoglobulins. It expresses immunoglobulins on its surface.