Pfizer's target measures for efficacy (see the study on clinicaltrials.gov) seem to be:
Confirmed COVID-19 in Phase 2/3 participants without evidence of infection before vaccination
Confirmed COVID-19 in Phase 2/3 participants with and without evidence of infection before vaccination
From Pfizer's study plan (VE = vaccine efficacy):
VE will be estimated by 100 × (1 – IRR), where IRR is the calculated
ratio of confirmed COVID-19 illness per 1000 person-years follow-up
in the active vaccine group to the corresponding illness rate in the
placebo group from 7 days after the second dose. VE will be analyzed
using a beta-binomial model.
(note: they also have other time windows and checkpoints in their analysis plan; which one is reported will shift from press release to press release as they get more data. If you are interested in the details the study plan also describes the planned interim analyses, and some of the press releases discuss deviations they've made from their original interim plans in consultation with regulatory agencies)
This measure is called relative risk, and can be written like this:
%InfectedPerTimeplacebo = NInfectedplacebo / (NStudiedplacebo * AverageFollowUpTime)
%InfectedPerTimevaccine = NInfectedvaccine / (NStudiedvaccine * AverageFollowUpTime)
Efficacy aka VE = %Infectedvaccine / %Infectedplacebo
If you assume risks are the same in the placebo and vaccine groups (they "should" be, but might vary if, for example, people who experience vaccine side effects change their behavior) and the average follow-up time is the same (they should be approximately the same, because they are giving the vaccine and placebo to patients enrolled at the same time), this ratio would tell you that a vaccine efficacy of 95% means that if you took 20 people who would have had a positive test after the placebo, you would only expect 1 of them to test positive if they instead got the vaccine.
Population vs. individual statistics
Put very simply: is it 100% effective in 95% of the population, or 95% effective in 100% of the population?
These are population-based measures. They can't say anything about efficacy in particular individuals by these outcome measures. For example, there is no way to know from a study like this whether the vaccine is 100% effective in 95% of the population, or if it raises the infective dose in everyone by some amount which causes the number of people exposed to this critical viral dose in their environment to decrease by 95% (or some other effect with the same end result).
Other approaches like challenge studies, where vaccinated individuals (or animal models) are intentionally exposed to a certain dose of the virus, can help understand the individual effects of vaccination, as can indirect measures of immune response like antibody titers. These approaches have other drawbacks, however (safety, translating animal results to humans, translating a given immune response to an infection chance, etc).
Beyond just 'vaccine efficacy': disease severity, real-world efficacy
These particular outcomes also say nothing about disease severity. It could be that the people who do test positive despite getting the vaccine get just as sick as the sickest people who don't (interpretation would be that the vaccine protects mostly against mild illness). It could also be the reverse, and that people who get the vaccine and still test positive have a milder illness than they would have otherwise. Efficacy defined by this relative risk ratio does not say anything about this, it only compares positive vs negative rates.
An additional note: these numbers report efficacy in the trial environment. "Real-world" effectiveness (the same measure of effect, but in real world use rather than under trial conditions) might depend on other factors such as differences in the people enrolling in trials vs the general population (both in terms of things like age and preexisting conditions as well as behavior and exposure risks), failure to administer the vaccine properly (including improper storage), failure to complete both doses in timely fashion, etc. This measure of effectiveness also refers only to "primary" effectiveness. One would expect that if enough people were vaccinated, the effect on the population could far exceed the primary effectiveness, because not only do vaccinated individuals have a lower chance of infection, but everyone else in the population also has a lower risk if there are fewer people available to transmit the infection.