Each B-cell has unique antigen receptors (called B-cell receptors, or BCRs) on its surface and responds to one specific antigen (hypothetically).
B-cells are produced by stem cells in the bone marrow (as are T-cells) and remain in the bone marrow to mature (T-cells mature in the thymus).
Maturation includes eliminating self-reactive lymphocytes; for T-cells maturation also includes eliminating non-reactive lymphocytes.
B-cells that don't recognize host tissue as "self" and are potentially harmfully reactive are eliminated during maturation by undergoing apoptosis. This process of eliminating self-reactive B-cells is called clonal deletion.
After maturation, B-cells leave the marrow and move to lymphoid tissues, where they are most likely to encounter pathogens that are more susceptible to the humoral immune system