PGA stands for "Professional Golfers' Association". There are many national organisations of that name including:
Originally, PGA's were the central bodies for all forms of professional golf in their territories, but now some of them, including those of the United States and the United Kingdom and Republic of Ireland, are focused on the needs of the majority of professional golfers who work as club or teaching professionals, as opposed to being tournament professionals.
The two largest professional golf tours in the world, the PGA Tour and the PGA European Tour are now independent of the PGA's which established them.
PGA of America
The PGA of America was founded in 1916 in New York with 35 charter members. Since its inception the PGA has grown into the largest sports organization in the world with more than 28,000 men and women golf professionals.
Information from http://www.pga.com/home/pgaofamerica/pga-history.cfm
