What is the medical term meaning type of immunity where memory cells are formed?

Adaptive Immunity is the type of immunity that creates memory cells. This is a specific type of immunity that reacts to the "non-self" antigen of pathogens. In the initial or first introduction to the pathogen, Immunoglobulin M (IgM) predominates the circulation. But in thesubsequentintroduction of the same pathogen where in memory cells were already formed from the previous event, Immunoglobulin G (IgG) now predominates. These antibodies either neutralize pathogens directly, or signals the complement system and/or the Natural Killer cells to eliminate the pathogen.

Since memory cells are already formed, the body is better equipped in dealing with the same pathogen the second time around.

This is the same concept in vaccinations, wherein we introduce into the body the same pathogen but in a weakened form removing it's virulence.