The social security systems inside the European Union are not unique system. The European Union respectively the countries that signed the contract of the union decided not to build one system for the whole union but to coordinate the different social security systems of the member states to ensure one of the essential cornerstones of the union the free movement of persons (workers) inside the union.
The basic principle of social security is that a worker is insured in the country where she/he is doing the work. E.g., if a German is working in Belgium she/he is insured in the Belgium social security system. This rule would also apply if she/he has a German employer and the latter sends him to work in Belgium. Because the employer in Germany has to insure the worker also in Germany the worker has a double insurance (in Germany and Belgium).
And there comes the A1 form into the game. This form is the tool to coordinate the social security systems and help to avoid such doubled insurance. If – like in the above example – a German employer sends his employee to Belgium he had to apply the A1 form (https://europa.eu/youreurope/citizens/work/social-security-forms/index_en.htm) before the employee went to Belgium. The employee has to carry at least the A1 application with him, once he left Germany and enter Belgium (regularly he should own the A1 form in this situation).
The application for an A1 is a duty of the employer. He has to submit this application to the competent social security institution of his place of business, in the example the one in Germany.
If the authorities of the other state (in the example the Belgium authorities) came across the German employee without an A1 form (or at least the evidence of the application for an A1) they will hand out a punishment to the employer. This fine could be very expensive and is regularly not refundable.
It is current opinion among employers that an A1 form is only needed for longer foreign work periods, but that is not a correct interpretation of the European regulations. The employee needs an A1 form for every work, he was send to another country of the European Union (or a country where the regulation of the European Union are effective, e.g. Swiss or Norway). Thus the employee needs such a form too, if she/he makes a business trip only for a very short time into the other country, e.g. only for an hour or hours (https://www.krankenkassen.de/ausland/portable/a1/ , https://www.haufe.de/personal/entgelt/meldeverfahren-a1-bescheinigungen-kuenftig-maschinell_78_378230.html), e.g. visits an event, a conference for an hour or hours on behalf of his employer (regularly within his working hours, work contract).
The need of an A1 form is not narrowed to employees (and employers), it applies to self-employed people too, if they cross the border to do their work in another country of the European Union (or the countries where the coordination rules of the European union are effective).