Once you have been exposed to an antigen, you develop immunity against the same antigen because

Because an antibody is "made" relative to the antigen, but kept at low levels when you are exposed the first time ("primary immune response"). The second time you're exposed to the same antigen, memory cells recognize it and the body produces a high level of antibodies, and the level of antibodies usually remains higher for a longer time ("secondary immune response"). This is your basic immune response (primary and secondary).

This explains exactly why vaccines are effective to extremely effective.