Answer:
A HOA is a corporation -- usually a non-profit -- that operates the real estate property that all owners own in common. The corporation is led by a board of directors which is elected by the membership -- owners.
When you purchase a unit -- or home -- in such an association, you are obligated to live within that private democracy according to the covenants, conditions, restrictions and rules (CC&Rs) in force for the association. By-laws and amendments also apply.
The association pays its operational expenses with funding from assessments that every owner pays annually, usually in monthly increments.
Another Answer
Home-owners (persons who own their house) associate (get organised) to fight for their common interests.