The boss was originally designed to deflect blows from the centre of round shields, though they also provided a place to mount the shield's grip.
[1][2] As time went on and heater shields with curved bodies became more popular, and enarmes superseded the bar grip, the boss became more of an ornamental piece.
A boss provides a significant advantage for deflecting blows when using a punching motion, but is not very effective when using a pivot to block an attack.
First found in prehistoric bronze, in medieval times, shield bosses were made by armourers out of sheets of iron or steel.
The armourer started with a flat, relatively thin sheet and sank the metal into a bowl, which might then be planished and polished.