Heritable Priming is the name given to the process in which organisms are able to pass-on stress protection from the parent generation to the siblings.
The 'stress' can be physical (one of the original studies investigated how plants' lack of water can protect later generations from drought stress) or bacteriological / viral.
It has been discovered in a very wide range of organisms, from plants, to invertebrates to mammals.
A 2020 paper in Nature describes the process :
Parental exposure to pathogens can prime offspring immunity in diverse organisms. The mechanisms by which this heritable priming occurs are largely unknown.
Multigenerational responses to environmental stress have been reported in evolutionarily diverse organisms. These studies investigated a variety of types of stresses ranging from osmotic stress, to mitochondrial stress, to pathogen infection. In each case, parental exposure to stress appeared to prime offspring to respond to a similar stress.
See : Nature Communications volume 11, Article number: 1741
If such mechanisms can (or do) work in humans, the implications for healthcare and immunity protection are substantial.
Whether environment-driven transgenerational responses exist in humans has long been a hot topic for debate. However, since it is hard to acquire the relevant data for population studies, the answer is still in the air.
Note: The process is separate from the way that antibodies, for example, can be passed from parents to offspring. Instead, the mechanism somehow alters the genes of parent, and these changes are passed on.