Re: How do B-cells become specialized for certain viruses?

Excellent question!
B cells have cell surface antibody that they use to recognize antigens 
such as viruses (see Figure, which is from “Immunology, Fifth Edition, by 
Goldsby, et al.). After contact with the virus, the B cell can divide and 
become either a plasma cell, which secretes antibodies to neutralize the 
virus, or a memory cell, which gives you better protection in case you 
get infected again by the same virus. 
Two important things: 1) Each B cell has only one “specificity” meaning 
that all its cell surface antibodies recognize the same antigen. 2) You 
make millions of B cells a day and each one can potentially recognize a 
different antigen. So when you get infected with a virus, only those B 
cells that can bind to the virus become plasma cells and memory B cells. 
This is called clonal selection, because the antigen (virus) selects the 
B cells making the right antibody to respond.