Expertise
Immunology
What the immune system actually remembers after an infection or a vaccine, and why the second encounter with a pathogen looks so different from the first.

Described in words
After a first exposure the immune response rises slowly and modestly. After a second exposure to the same target it rises much sooner and reaches a substantially higher level.
The immune system is often described as an army. It is closer to a filing system that learns: it keeps a record of things it has met before, and that record is what makes a second encounter faster and less costly than the first.
Almost everything useful about vaccination follows from that one fact — and so do most of the honest caveats, because a record can fade, and a pathogen can change enough that the record no longer matches.