A nicely done news article about what we do and don't know at this stage. From the conclusion:
In the end, the vaccines likely limit transmission in two ways:
1. Preventing some percentage of infections totally, even asymptomatic ones. This prevents the body from replicating the virus and having enough to share with others.2. Turning a further percentage of what would have been symptomatic infections to asymptomatic ones, thus preventing the body from coughing, sneezing and generally shooting the virus long distances.Overall, I think it would be reasonable to estimate that vaccines reduce transmission from anywhere from 30% to 90% — a huge range, to be sure, but it depends on the vaccine used and the accuracy of these studies with limited sample sizes.
That result would be both good and bad. On one hand, it’s not total sterilizing immunity — someone who has been vaccinated still has a reasonably high likelihood of picking up the disease at a party and giving it to their immunocompromised friend later in the week. That means the vaccinated probably shouldn’t go to parties where there are unvaccinated people while the pandemic rages.