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.
Declaiming the Claim will not return any items to you, nor any Silver Pieces used to expand the claim.