What exactly does it mean for a vaccine to be 95% effective?

When they say a vaccine is 95% effective, does that mean 95% of the people are immune, and 5% have no immunity? Or does it mean each individual still has a 5% chance of getting infected? Or something else?

I don’t want to give the wrong answers, so I’ll say the answers are buried in these two links:

https://www.nejm.org/doi/full/10.1056/NEJMoa2034577?query=featured_home

Oxford–AstraZeneca COVID-19 vaccine efficacy

The good news in that effectiveness in preventing severe disease appears to be near 100 percent.

Not so good news is that they didn’t always test for virus shedding often enough to say what the efficacy was in stopping transmission.

The back of the envelope explanation is this. The two groups had almost exactly the same number of participants. There were 8 detected cases of covid-19 in the vaccinated group and 162 cases in the placebo group. Under the assumption that in two groups of the same numbers of people in very similar circumstances there should have been the same number of covid-19 infections in both groups, then you can say that the vaccinated group is missing 162 - 8 = 154 infected cases, for an efficacy of 154/162 or 95%.