Vaccines are made to target a specific or a specific set of pathogens.
The background states that when you gain immunity to the target pathogens, that’s called “antigen-specific adaptive immunity.” When you gain immunity to pathogens similar to, but not, the target, that’s called “cross-protective immunity.” Sometimes, vaccines provide “beneficial off-target (heterologous) effects that alter immune responses to, and protect against, unrelated infections.” It has never been tested if mRNA vaccines also show a similar benefit.
So the study has concluded that children who received the BNT162b2 mRNA vaccine showed increased immune response to pathogens unrelated to COVID-19. Meaning that when children take this vaccine, they are less likely to die from other pathogens too! Which sounds pretty awesome.