In a primary immune response the active immune system must first recognise the pathogen via B-lymphocyte cells with antibodies on their surface that are complementary to the antigens of the invading pathogen (clonal selection), this can occur via an antigen directly binding to the B-lymphocyte receptor or a T-lymphocyte activating it. Once this occurs the B-lymphocyte divides (clonal expansion) and then differentiates into a plasma cell that produces antibodies at a high rate. This process takes a few days.
In a secondary immune response (reinfection) many complementary B-memory cells left over from the primary response are already in the bloodstream and rapidly recognise the pathogen. They divide and differentiate into plasma cells that produce antibodies at a rapid rate quickly killing the pathogen. Thus, the end result is that pathogen levels decrease faster in the secondary immune response and antibody levels rise faster and higher (explain this via drawing out a graph).