How does the regulatory body CAA link to aviation?
Brief answer: The CAA ensures that all flying in the country, be it small planes, or major airlines, are acting in accordance with policies, standards and aviation law. These standards and laws are written by ICAO (International Civil Aviation Organisation), and presuming you are referring to the UK CAA, standards and policies can also come from EASA (European Union Aviation Safety Agency). Any differences in the standards, policies and laws from ICAO are listed in the CAA's AIP
These standards, policies and laws which the CAA are responsible for regulating cover a wide range of areas: pilot's licenses to meteorological equipment and standards, rules of flying in the air (e.g. distance from cloud, filing flight plans) to aviation medicals, charts and NOTAMs to compensation claims, drone safety at airports to aircraft design and parts, airport lights and signs to air traffic services available... [the list goes on...]
Basically, anything related to flying, the CAA will govern according with international rules written by ICAO (and EASA).