The influenza virus is a tough critter to combat. It changes shape too often for effective vaccines to train the immune system to recognize all the possible shapes. That's why we need a new vaccine each year, targeted to the strain that the authorities guess will be predominant.
The problem is that the immune system recognizes the overall shape of the virus in order to attack it. A key molecule that immune systems 'see' is the protein hemagglutinin (HA), which is located on the virus surface (the blue and red mushrooms in the figure). The name comes from the fact that this kind of molecule can cause blood cells to coagulate when exposed to it, the details of which are unrelated to this post.
The HA molecule binds to a sugar-related molecule on host cells' surfaces, and the virus then pops into the cell where it can proliferate. There are many variants, or strains, of HA, numbered H1 to H16 etc., and a vaccine must be targeted to the specific characteristics of the strain that you want to be protected against. The strain variation targeted by traditional flu vaccines is in the blue or 'head' part of the HA molecule as seen in this figure.
A general flue vaccine would not have to be targeted to any given HA variant. It would in principle lead your immune system to recognize all strains, but that's not how flu vaccines have worked so far. However, a new tactic may be about to bear fruit. Part of the HA molecule is apparently not as visible to the immune system (shown as the red stems under the blue head in the figure), but it doesn't vary nearly as much as the head of the molecule--apparently, if it changes, the virus's protein coat won't form properly. This conservation of structure makes this a vulnerable region in the virus. The new strategy would target the stem, perhaps along with a seasonal supplement for a specific HA strain when/if needed. The hope is that this will generate broad long lasting, or even lifetime, immunity after a single vaccination in early childhood. Here is a release from Gary Nabel at NIH who is one of the investigators, explaining the approach, although we cannot yet find a detailed description of how the vaccine allows the immune system to 'see' the HA stem.
This is an evolutionary approach to vaccination because it targets the part of HA that is conserved, presumably by strong natural selection. You attack the pathogen at a place it cannot easily vary, so it can't quickly evolve a defense. Exactly why the HA stem section cannot vary very much is probably known, but not by us--perhaps it has to do with the proper assembly of the virus's protein packaging--all the coat proteins must fit tightly together, etc. There would thus be no stem-variant viruses that could take the place of those destroyed by the vaccine-boosted immune system.
Why natural immunity does not also generate antibodies that recognize the stem is an interesting question. Virologists may know the answer.....but we don't.