Obedience means that units are compelled to obey orders. Some may disobey if they believe the order goes against higher orders or their Ruler's interests Erf-b1-p005. Disobedience may cause the unit to disband.
Orders enforced by Obediance are not limited to ones involving strategy and combat. In fact, nearly any command comes under its purview, including demands for sexual favors. The Earth idea of not taking advantage of a unit's obedience in this way is alien.summer-updates-044