The body's process of becoming resistant to a particular disease after acquiring the disease from a vaccination is termed:

Acquired immunity

Explanation:

Based on the information provided within the question it can be said that the term being mentioned is called Acquired immunity. This term (like mentioned in the question) refers to an immunity that the body learns when the individuals immune system runs into unknown invaders and manages to recognize antigens. Allowing the body to slowly become immune to those invaders that are attacking the immune system.