There are many different meanings for the acronym APA. However, because of the subject matter of your previous questions, I assume that you are talking about the meaning of this acronym in the area of administrative law. In this context, the acronym stands for the Administrative Procedure Act. This was a law passed by Congress in 1946.
In our political system, bureaucratic agencies have a great deal of power. Congress writes laws that are not very detailed or specific. These laws give a great deal of discretion to the agencies because the agencies are empowered to write rules based on the laws. These rules have the force of law. This is particularly important because the size of our government has increased dramatically over the years. This means that administrative agencies can have a great deal of impact on our lives.
The growth in the importance of the bureaucracy really took off during the New Deal. Many government agencies were created. This caused the government to see a need to write laws to govern the actions of those agencies. This was the purpose of the APA. It was written as a way to set out procedures that all government agencies would have to follow when proposing regulations.