Proc Coefficient (a.k.a. PC, or Proc Rate) is a game mechanic in Diablo III used to compensate for some skills' ability to hit multiple targets with a single cast, or to deliver multiple hits to a single target.
All skills have a Proc Coefficient between 0 to 1, which controls the effectiveness of certain 'on hit' affixes, like Stun on hit, for that particular skill. The coefficient reduces either the effectiveness of the triggered special property (such as the amount of Life regained from Holy Cause), or the chances to trigger this effect, if plainly reducing it is not possible.
For example, a skill with a Proc Coefficient of 0.3 will turn a 10% chance on hit into 3% per hit per target (10% x 0.3).
Typically, skills that can only hit one target will have this coefficient equal (or very close) to 1, meaning the affix will trigger ("proc") on (nearly) every hit. Some skills, usually those that deal damage independently from the player's actions, like pets, have a proc coefficient of 0, meaning the skill will never proc an 'on hit' affix. Damage over time and area of effect skills generally have very low proc coeffients, but since they can hit many targets at once, or the same target many times in succession, this is more or less balancing the total chances.
A basic attack always has a PC of 1, regardless of the weapon type equipped.
The PC only affects special effects, and not the damage done. Area Damage and many other effects also ignore PC.
Each skill's own 'chance on hit' effects, including those that are granted by the skill runes, are generally not affected by the Proc Coefficient; however, chances given by passive skills and items typically are.
For a full list of each skill Proc Rate of every class, see D3 Max Stats or any other on-line chart.
As of patch 2.1, Life on Hit is unaffected by the Proc Coefficient: it restores a fixed amount of Life regardless of the skill used and amount of enemies hit. Each skill either can or cannot trigger it.