It's really not all that similar. The emphasis is very much on the local government, more so than really anywhere else in the world (that I know of). There are some states where local governments matter. There are more where power is concentrated at the level of the county or state government.

A (bad) way to think of it would be something along the lines of a New England townhall system on steroids, with several layers of federal/confederated associations above the local township (geminde).

Again, not a great comparison, but it's something that at least a portion of the US-centric users on here would know a little about.