Vaccines are not magic. Yes, calling people "immune" and "protected" is just bad use of language. No one is truly immune to a virus for which they were already infected or were vaccinated against.
Nothing can create a magic forcefield around you that stops airborne viruses from being breathed into your nasal passages and lungs (except maybe being isolated on a mountain top or a deserted island). When the virus lands, it will infect and attempt to replicate in an exponential fashion.
If this is a new virus to you, you're body has a few days to a week to find the right protein pattern through trial and error that will dismantle the virus before the virus destroys enough of your organs that you're dead. Anti-viral medications can slow down the replication of some viruses, but, in the end, it will be your immune system that will save you.
Rather than hoping your immune system will work fast enough to kill the virus before the virus kills you, you can train your immune system to 'recognize' the virus and have enough immune cells that know how to kill the virus ahead of time. That can happen in two ways:
1. you already were infected with this virus, and your immune system fought it off
2. you received a vaccine, which tricked your immune system into thinking it was a real virus, which caused the immune system to be ready to fight off the real virus if ever you were infected
The vaccine does not stay in your body. It is not sticking around ready to fight off the virus. It is destroyed by your immune system and excreted like any non-welcome chemical in your body (e.g., like with alcohol). Instead, your own immune system is primed and ready to fight off the virus.
And your immune system isn't magic, either. It does not create a forcefield around you keeping viruses from being breathed in. What your immune system does is fight off the invading virus. If you had the virus before, or the vaccine, then your immune system is ready and ahead of the game.
This is why one can be re-infected ("breakthrough infection") even if you've been vaccinated, and even if you've had the virus before.
So, what good is the biological immunity from vaccination or a previous infection?
1. It dramatically increases the likelihood of preventing "serious disease" (defined as having to be hospitalized), or
2. Dramatically increases the likelihood of not being killed by the virus.
A complication to this is that viruses mutate into various "variants." These variants can sometimes be more adept in evading your immunity cells. And so, you get reinfected more easily. Such is the case with the Omicron variant.
However, the Omicron variant, as much as reinfections are spiking in the general population, hospitalizations and deaths **aren't spiking.** People's immune systems from vaccinations and previous infections are still mounting a good defense.
Also, with everyone going maskless and being less prone to viral-prevention routines, the virus can spread faster.
There are a lot of people being reinfected again and again without even knowing it because they are asymptomatic. The virus is there but not able to do enough damage to notice in symptoms. We only know this from people whose jobs require regularly being tested, like healthcare personnel, athletes, politicians, and, yes, even Dr. Fauci.
