Not all neighborhoods have an HOA. In my area, condo and townhomes all tend to have a homeowner's association (HOA), but also some single-family communities, too. My area has 4 associations under a master HOA -- the original townhomes (where I live), a condo building, single family homes, and a new townhome section that has their own HOA. Across the street is a neighborhood that has no HOA, just a committee that handles maintenance of the entrance to their neighborhood (signage and plantings).
In the 4 communities where I live, there are rules and regulations that were approved by the first governing board and stipulate how the community association is set up, managed, and the documents lay out owner vs. association obligations. For example, it sets out who is financially responsible for grounds and exterior maintenance, painting, and roofing; it defines common areas (association maintained) and limited common areas (like my deck, since it is only accessible from inside my unit), and what colors must be used on exterior doors, trim, and railings, should the owner want to do their own painting; what may be planted in-ground and who is responsible for non-association plantings, etc.
For the holidays, the HOA stipulates when holiday decorations may go up and when they must be taken down (30 days before / after) the major holidays that are celebrated within our neighborhood. For Christmas, this is to insure that your creche or blow-up Santa on the front lawn is removed before Valentine's Day or Easter. For Christmas, because we may have snow, we need to keep any decor away from sidewalks and steps, so they don't obstruct snow removal. There is also a time when exterior lights must be turned off (midnight?), so they don't impact neighbors.
Each HOA makes the rules for their particular neighborhood and its needs. They are primarily designed to help maintain uniformity and to keep up property values. Our "master" HOA insures that each HOA operates within a similar set of documents, and it handles maintenance of the entrance areas, grounds for the entrances and center medians, on our two major roads. They also handle water and electric lighting for those areas, as these elements and their costs are shared by all 4 HOAs. Does this make sense?