The claim is an object on the board that holds objective items like gold nuggets in the Claim Jumping scenario. A number indicating how many gold nuggets a claim currently holds always floats above it. The claim is also the starting point for a player's units in the game, although they may appear some distance away, depending on the map.
To deposit a gold nugget into a claim, a unit holding one must walk onto a tile adjacent to your claim (it is possible for an air type unit to deposit nuggets from directly on a claim's tile.) In claim jumping, it is possible for an opposing unit to remove, or "steal" a gold nugget from a claim by moving next to it.
In the Gold Rush scenario, the claim is represented by a cargo tank and cannot be stolen from, but is otherwise identical in function.
In Cattle Rustling, the claim is represented by the rustling post, and the number above it represents the number of cattle wearing a brand.