A Homeowners Association (HOA) is a group of homeowners in a common building or common subdivision that are responsible for community rules and common area maintenance.
HOA rules are imposed by the HOA board and often voted on by all of the homeowners in the community. In addition to community rules, HOAs are usually responsible for maintenance of common areas like hallways, courtyards, pools, etc. The HOA funds maintenance by charging homeowners a periodic assessment, usually monthly.
HOA rules and bylaws, usually called CC&Rs, are bound to the property on its title. When an owner sells a property, they cease to be a member of the HOA and the new owner is forced to become a member.
Read more about how to evaluate a Homeowners Association.