Antibodies are produced by B cells, mostly by plasma cells, in response to signals from other cells of the immune system. They are also known as immunoglobulins and have a Y shaped structure.
When the immune system encounters an antigen for the first time, T cells provide help to B cells which become capable of producing antibody with high affinity and specificity for that antigen. The primary immune response eventually leads to the generation of memory cells with high specificity for that antigen.
Upon later encounter with that same antigen, the more rapid secondary immune response occurs. This is enabled by the activation of the previously generated memory B cells which produce a large amount of antibody specific to that antigen in a shorter time than the primary response. Overall the secondary immune response is more effective than the primary response.