That statement's missing a comma. It should read:
"Vaccination is a medical procedure, which carries a risk of injury or death."
ALL medical procedures carry a risk of injury or death, even something as simple as putting on a bandaid. Vaccinations are nothing special here.
When I was a kid, whooping cough, diptheria, measles, and rubella were all fairly common. Kids got them all the time. And some of those kids died. Now you never see them. Kids that would have died are staying alive.
Smallpox has been gone for 25 years or so. Polio is on track to be eliminated within a few years (ask someone who can remember the 1950s about polio). Both because of vaccinations.
You just have to ask yourself what are the odds of anything happening if you don't vaccinate versus the the odds of anything happening if you do. And try to keep the risks in perspective. For example, the single most dangerous thing that people do to their children they do all the time without even thinking: they take them for a ride in their car.
The anti-vaccination movement is a fairly recent development. It arose around the time that the epidemics of the recent past faded from memory. But the thing to remember is that the epidemics were eliminated by those very same vaccinations.