What is valve seat countersinking tool?

This is called a reseating tool and is used to grind away cracks on the seat of a tap or valve.

There is an issue here that is not being discussed. If you grind the valve seats, for what ever reason, you must grind the valves also, otherwise you will not have a matched valve and seat assembly. Doing one without the other, will be a learning curve you don't want to experiment with. If the valve and seat do not match perfectly, your just spinning your wheels as the end result will be a whole lotta work for nothing. When you think about the massive pressure's and extreme heat that is created during the combustion process, that last thing you want is a set of mismatched valves, trying to hold it in the cylinder area. Also lets not forget about the fact that when you grind a valve seat, your allowing the valve to seat deeper into the head and the last time I checked they don't sell valve stem lengthening kits. You are not moving the camshaft, it stays the same, but the valve stem moves farther away from the cam when you grind the valve seats. So if ya hear a bunch of clackey valves when you first start the engine, you will understand why they don't sell valve lengthening kits.