If a model has a characteristic of '0', it has no ability whatsoever in what the characteristic represents. This is seen most often with Ballistic Skill, as many models simply lack the ability to make any form of ranged attack.
If any model or object has a Weapon Skill of 0 then it is unable to defend itself in combat, and any blows struck against it will therefore automatically hit. If at any time a model's Strength, Toughness or Wounds characteristic is reduced to 0, it is slain and removed from play.