Passive skills are in opposition to active skills. Passives are skills that add bonuses all the time, once points are placed into them. Passive skills are not used directly for attacks, and tend to provide bonuses to numerous other skills, or add percentages to damage, to/hit, defense, resistances, and other useful stats.
Passive skills are often as or more important than active skills, but usually receive less attention since they are not flashy or obvious in their effects.
Passive skills seldom possess synergistic properties. Passive skills are not signature skills.
As of Blizzcon 2008 (November), there were far more passive than active skills in the three character trees. This may or may not change during the course of development.