I think the Pfizer/Moderna vaccines in particular are known to trigger side-effects in a lot of people - and to trigger severe (that potentially keep you off work for a day or two) side-effects in more people than we're used to with flu jabs for example. The Moderna jab in particular has something like 10% of people experiencing severe fatigue after the second jab.
The numbers were released as part of the clinical trials Phase3 report, but as those are really long documents I'll link to a press report instead:
https://www.vox.com/22158238/covid-19-vaccine-side-effects-explained
As Pogue said - some people get flu like symptoms (fatigue, headache, joint pain etc). Mostly mild, but in a significant number it's more severe (but generally shortterm). I've read some of the vaccine advisors commenting that for a hospital (for example) it would be better not to vaccinate all the staff in a particular department on a single day - just to reduce the odds of having a bunch of people absent or unable to work normally the next morning.