If you've had something lost or Stolen or you want to know whether something you're planning on buying or have bought may be stolen you can check to see if it's been reported stolen through online websites such as
https://www.stolenregister.com/
That's just one website that you can check for stolen items with the serial number but I'm sure there's other websites that allow you to look up something as stolen or lost by the serial number.
The police can also check to see if something was stolen through the serial number in case the item has been reported to the police as stolen.