To explain it as best as I can, if this sounds condescending I apologise in advance.
There is a massive security issue in the world, governments around the world raise concerns and they go to the UN Security Council to try and sort it out and make a unified response to the problem. Air Transport is essentially the same as a world security incident, abstract I know but I will explain.
ICAO is the world standard but for it too be enforced by that level would be very difficult. It would be expensive as it would be centrally located (say New York) and dependent on national laws and standards would be difficult to enforce legally. so we know go down to national standards.
In the UK this is the CAA, adopted by government and operated within UK law but adhered to ICAO standard. CAA enforces rules and regulations and inspects facilities to make sure that standards are met. They would also keep a very close eye on the airlines as well.
Know you are from Minsk, Belarus is a part of EASA (European Aviation Safety Agency) which covers the EU https://en.wikipedia.org/wiki/European_Aviation_Safety_Agency. Also the UK is part of that organisation as well. So in some countries you will a national, regional and international body overseeing regulations and safe practices.
I hope that made sense, its a little difficult to go into as its a lot of jargon to explain. For me its not too bad as I did Military Flight Ops and ATC for 16 years.