If you look at any land title, you will see that they almost always exclude mineral rights. The land owner only owns the surface. The government owns the minerals
underground.
A mineral claim is a registered legal right to exploit the government's minerals under a piece of land. If you have a mining claim on a parcel of land, you have the right to access that land and dig for the minerals. You can
sell the minerals you find, though you will likely have to pay the government a royalty.
Most mining claims are filed on government land. However, there is nothing stopping someone from filing a claim under private land, which can cause grief for the surface property owner.