An HOA is typically formed by people who live in the neighborhood to allow a housing development to represent itself as a single larger entity instead of several smaller ones.
Like any human collaboration they can be awesome or terrible. A good HOA can manage resources for ammenities like pools and sports courts, they can help homeowners settle disputes over things like fencing and street parking. Like many volunteer orgs, they're run by those willing to volunteer - which are not usually the most capable at the job.
At the end of the day HOAs do get a lot of heat because they often enforce community guidelines on things like mowing your lawn and not painting your garage door to be the nazi flag. Like anything, this is a tradeoff - you may want to run a ham antenna in your backyard and be told you're not allowed.