Its a private association formed when a residential subdivision is developed. It sets up rules that the owners must follow in maintaining their homes. No junk in your front lawn. You might need to get prior approval for changing the outside of the house. Often times there is a monthly fee that goes towards landscaping or common amenities like pools. You agree to these terms when you acquire the home and subsequent buyers must do so also. After most of the homes are sold, the homeowners elect a board to run the association. Sometimes the members of the boards can be power hungry and vindictive. The homeowners can all vote to end the association at some point so older single family homes tend not to be under an HOA.