I wish that the developers had not called the jab a vaccine, because previous vaccines have prevented the vaccinated catching the illness. When we had the smallpox, tb, diphtheria, polio jabs as children, they gave 100% protection. You could sit beside a tuberculosis sufferer coughing their lungs out in perfect safety.
This is complete rubbish. You can look up the effectiveness of those jabs quite freely and none give 100% protection. They give very good protection, which is probably why you never caught the illness, because they reduced numbers in the population sufficiently so that there weren't epidemics of those illnesses going around.
The covid jabs are around 95% effective just from a very cursory google - that might be . When you have an epidemic, 95% is helpful, but means 1 in 20 people are still going to catch it. When you have so much of it going around the general population that means you're still likely to get it but it will take on average 20 exposures before you get ill.
I honestly think we should stop using percentages when talking about probability, because they don't seem very well understood in this context. It's seen as a kind of scale from 1 to 100, where 1% means "incredibly unlikely, almost impossible" and 99% means "almost certain". It doesn't, it means 1 or 99 out of 100. 1:100 chance means that something is unlikely to happen to you if you have one shot at it - for example a raffle with 100 tickets and you have one ticket. But if you enter ten of those raffles and you have five tickets for each of them, then you have fifty chances to win overall and that starts to look quite likely, even though the percentage chance of any one ticket coming out is the same.
It's the same with diseases. If you come into contact with polio once or twice in your lifetime, then the 99% effectiveness of the vaccine (or 95% if you had the oral one, which you probably did if you are over 30) will serve you very well, because you'd only have a 1 in 100 / 1 in 20 chance of catching it. But if you come into contact with covid several times a week, which is likely in the current situation, you'd actually need a vaccine that was 99.9% effective (1:1000 chance of failing) to be as effective as the oral polio vaccine or 99.98% (1:5000 chance of failing) for the jab over the period of just one year.
99%, 99.9% and 99.98% don't "feel" significantly different unless you are very well versed in probability and statistics, even though these are wildly different chances, which is why I don't think we should be using these in the context of public health messaging.