Is it just a shorthand for "the adult population was not subjected to these patogenes during childhood and is therefore more susceptible to them" or is there maybe a certain genetic component to it?
It's a little of both. You can read some of the math behind this in Infectious Diseases of Humans: Dynamics and Control, by Anderson and May. Chapter 2 gives an overview. The behavior of an epidemic depends a great deal on the specifics of the host-pathogen interaction, but generally you can say that the epidemic curve in a a naive population will have a larger and sharper upswing than in a previously exposed population. You can attribute some of this different behavior to lack of adaptive immunity in the adult population. Again, depending on the pathogen, you can also attribute some of this different behavior to lack of selective pressure in the naive population on highly variable loci involved in the immune response.
To address more directly what seems to be your primary question: yes, there is a genetic component to the susceptibility of a host (e.g., a human) to a pathogen (e.g., a microbe that can cause disease).
There are certain aspects of what we call the adaptive immune system in jawed vertebrates that are not directly heritable. You are a jawed vertebrate, and the DNA in each of your B-cells and T-cells that produces B-cell receptors (BCR) and T-cell receptors (TCR) goes through a number of changes outside of the germ line. You can read about these changes in, for example, How the Immune System Works, Chapter 3, by Lauren Sompayrac. It's an excellent introduction if this is new to you.
In addition to the exact set of BCRs and TCRs in the pre-immune state, your current repertoire of cells and molecules is determined by your history of exposure. While some of this can be vertically transmitted, the majority of it is not. This is one of the reasons why, when you look at this repertoire, much of the variability is attributable to non-heritable factors. A not insignificant proportion is attributable to heritable factors, though. So if TCRs and BCRs are not encoded in your germ-line, and your environment obviously has a strong influence on your current immune state, where does the heritable component come from?
All of the other proteins involved in the immune system response are encoded in the germ line, and are thus heritable. Some of them are highly variable, and since they are very important they are under strong selective pressure. You can see important changes in the population distribution of these loci over a relatively small number of generations. There are many other heritable components of an individual or population's susceptibility to infectious disease. There is a great deal of work on this. Casanova has a great article about this in PNAS, which I've linked to in another answer to a related question. A more traditional review of his is here. Of course, he's not the only one working on this. I just like the way he writes. Here's a good one by Baker and Antonovics.
A simplified and speculative example
Re: your comment about measles in the Polynesian islands, we don't have scientific consensus about the relative importance of non-heritable and heritable factors for this particular case. Instead of getting into the nitty gritty details, I'll walk you through a hypothetical:
Imagine an isolated population with a lot of variability in germline genes that code for a special protein that helps their immune system mount a full response to viruses.
A very nasty, very contagious virus is introduced to this previously isolated population. The characteristics of the population help determine the outcome of their interaction with this new virus. Here are 3 important characteristics:
Because nobody has ever been exposed to this virus, nobody has neutralizing antibodies or the rapid immune response that happens the second time you're exposed to a pathogen.
Some versions of that special protein with all that variability don't do a good job of helping the immune system mount a response to this new virus.
Luckily though, some other versions of that special protein with all that variability do an especially good job of helping the immune system mount a response to this new virus.
Because of (1) the disease spreads broadly throughout the population. Because of (2), a specific group of people get especially sick, die, and (because they are dead) don't reproduce, and don't pass on their version of the gene that codes for special protein. Because of (3) a specific group of people do very well, are only sick for a little while, and do an especially good job at generating long lived immunity, and (because they are alive and well) reproduce a lot, and pass on their version of the gene that codes for that special protein.
The epidemic is eventually controlled. Years go by, and the virus starts circulating again.
Now the characteristics of the population are quite different, so the dynamics of the host-pathogen interaction will be different.
Many of the people that were alive during the first epidemic now have neutralizing antibodies and a memory response, so this second epidemic will not spread as quickly or as broadly. This is a non-heritable factor. Previous exposure to the virus has changed the repertoire of cells and molecules in people's blood.
Among the younger generation, more of them have the helpful version of the special protein that helps the immune system generate a response, so not as many of them will die. This is a heritable factor. Previous exposure of the population to the virus has exerted selective pressure, changing the frequency of the helpful and unhelpful alleles in the population.