Homeowner's Association (HOA) fees are charged for a variety of reasons, most commonly including: road and common area maintenance, upkeep of any bbq/picnic areas and parks, community signs, and a myriad of other features depending on what amenities your community offers.
As far as a monetary amount for HOA fees it can range widely, I've seen as low as $7/month all the way up to $120/month, it just depends.
Homeowner's insurance is completely separate from HOA fees and, just like your car insurance, has many options in terms of coverages and premiums.
I think they would only cover part of the insurance in the case of a common building, like in the case of a condominum development. In those that I am aware of those condominium HOA's cover only insurance for the structure and you are still responsible for contents and liability on your own (kind of like renter's insurance).