I assume it's an instrument for checking the alignment of the gun with the information being provided by the Gun Director and Transmitting Station. No idea how it works but there may be clues in: Historic Naval Ships Visitors Guide - Boresights and Boresight Telescopes Tim
We had bore sights in Challenger 1 tanks in the 1990’s ( chieftain before it also) I’m assuming the principle is the same Basically you place the bore sight in the barrel ( at the end) stand on a chair and look through it ( normally a 90 degree viewing lense) the gunner in the turret lays the sight at a target at 1000m. When the gunner says the gun is aimed at the correct spot the man looking into the bore sight can see if the gun and optical sighting system are looking at the same spot. Adjustments can be made within the sight until both are looking at exactly the same point. Make sense?! Alex.