It's not a binary thing... Vaccines make it significantly less likely that you will be infected, or if you are infected that you will develop the viral load necessary to be infectious, or if you are infectious, the period of time you are infectious for will be much shorter. At each step along the way the vaccine makes less likely that the vaccinated individual will infect someone else.

It makes it sufficiently less likely that if everyone was vaccinated, each infected person would, on average, go on to infect less than one other person, and the pandemic would end. The more people who are vaccinate, the lower that average of "people that get infected by each infectious person" goes. That is why vaccinations are important to everyone, not just the individual who is vaccinated.