The part of the immune system that destroys pathogens are the antibodies.
Antibodies are large protein molecules, each having a specific shape and binding site, similar to enzymes, which bind to the surface antigens of the pathogen and neutralize them. There a number of mechanisms through which antibodies achieve this, such as rupturing the cell membrane of the pathogen.
Antibodies also lead to immunity, if the antibodies to a certain pathogen are present, then the organism is immune to that pathogen.