Have a look at the missile and turret tracking damage from the EVE university wiki. https://wiki.eveuniversity.org/Missile_Damage#Missile_damage_formula and https://wiki.eveuniversity.org/Turret_Damage#Math
You can see that a higher signature radius will increase the hit chance for turrets and the applied damage for missiles. In both cases the painter will have more effectiveness when used on smaller and/or fast moving targets.
The entry for target painting explains about the painter improving things for the whole fleet https://wiki.eveuniversity.org/Target_Painter#Target_Painting
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