Small discharge, big damage
A static discharge you don't even feel yourself can already be enough to damage a component. Often such a part doesn't fail immediately but only weeks later, which makes the cause hard to trace. ESD gloves discharge the charge in a controlled way and are therefore the first link in an ESD-safe workplace.
Part of a bigger system
Gloves alone aren't enough: the floor, the workbench, the wrist strap and the shoes also need to be conductive. Also note that ESD is different from the antistatic requirement in EN 1149, which is about explosion risk.
