If you want a simple one-sentence description, I would HOAs are an example of the old saying about a beautiful theory being spoiled by an ugly fact.

Look and feel of the house, paint, Pool Management, Park (if the community has one, and not the city managed one) Management, Yard Management (Trees, Plants, Mopping, Trimming), Trash (overflow vs contained, when to put trash out, when to take your trash can back, to keep it out of sight from street view and such) Regulations on whether a house can be given to AirBnb and such, Single Family staying vs multiple family, cars that can be parked on the road and you can ask Chatgpt for more if you want.

Overall, with America being a capitalist country (and Florida state being the best example of it), they want people to keep spending their money on something, and would never allow someone to just 'settle' and live a life without spending money. HOA, among other things property taxes and other city imposed taxes you are never "resting in peace" after retirement, but wait for your next notice to come - either from City or HOA.

As a fellow European, preventing the value of your house dropping because your neighbors didn’t clean up their front yard.

Same function as the laws about when you can mow in Germany, simply at a sub municipal level.

There are HOAs in Europe. The Wohnungseigentümergemeinschaft comes to mind.

They empower grumpy assholes to play police and impose their will on you.

[dead]