Use this to claim an area as your personal property.
You can expand it, by spending Silver Pieces, through it's menu-interface when you right-click it.
You can have as many claims as you want, but only have one as homestead. All claims need upkeep of 4 + ('number of claimed tiles' / 300) per day. The claim stone can hold upkeep money for two months. The claimstone can be destroyed after the upkeep money runs out.
Right click on a claim stone to interact with it and see its current and max silver level.