The prefix (if any) always offers a bonus to the skill that it is associated with, as shown in the charts below. Skills that are boosted by class mods will also be shown in the skill tree selection, listing the number of bonus points from the mod and the final percentages for the skill.
A skill bonus however will not function unless the character has at least 1 point invested in the specified skill. Class Mod skill bonuses do stack, even if a specific skill is maxxed (5/5), up to a total maximum of 11 ranks in any skill. They are class specific upgrades that provide benefits to the character (or the entire team) by offering a wide variety of bonuses such as amplifying a character's damage, healing, increasing character health or shield capacity, reducing reload times, increasing skill ranks, etc. Class Mods, or COMs (short for Class Optimization Modules), are influential items in Borderlands 2.