A static ability is an ability of an object that is neither an activated ability nor a triggered ability; it is an ability that is always "on", and cannot be turned "off". Flying and fear are examples of static abilities.
Static abilities apply only when the object they appear on is in play unless the card specifies otherwise or the ability could only logically function in some other zone. Static abilities are always 'on' and do not use the stack. The ability takes effect as soon as the card enters the appropriate zone and only stops working when the card leaves that zone (or it says it does).
From the Comprehensive Rules
(Battle for Zendikar
(September 26, 2015
604. Handling Static Abilities
- 604.1. Static abilities do something all the time rather than being activated or triggered. They are written as statements, and they’re simply true.
- 604.2. Static abilities create continuous effects, some of which are prevention effects or replacement effects. These effects are active as long as the permanent with the ability remains on the battlefield and has the ability, or as long as the object with the ability remains in the appropriate zone, as described in rule 112.6.
- 604.3. Some static abilities are characteristic-defining abilities. A characteristic-defining ability conveys information about an object’s characteristics that would normally be found elsewhere on that object (such as in its mana cost, type line, or power/toughness box) or overrides information found elsewhere on that object. Characteristic-defining abilities function in all zones. They also function outside the game.
- 604.3a A static ability is a characteristic-defining ability if it meets the following criteria: (1) It defines an object’s colors, subtypes, power, or toughness; (2) it is printed on the card it affects, it was granted to the token it affects by the effect that created the token, or it was acquired by the object it affects as the result of a copy effect or text-changing effect; (3) it does not directly affect the characteristics of any other objects; (4) it is not an ability that an object grants to itself; and (5) it does not set the values of such characteristics only if certain conditions are met.
- 604.4. Many Auras, Equipment, and Fortifications have static abilities that modify the object they’re attached to, but those abilities don’t target that object. If an Aura, Equipment, or Fortification is moved to a different object, the ability stops applying to the original object and starts modifying the new one.
- 604.5. Some static abilities apply while a spell is on the stack. These are often abilities that refer to countering the spell. Also, abilities that say “As an additional cost to cast . . . ,” “You may pay [cost] rather than pay [this object]’s mana cost,” and “You may cast [this object] without paying its mana cost” work while a spell is on the stack.
- 604.6. Some static abilities apply while a card is in any zone that you could cast or play it from (usually your hand). These are limited to those that read, “You may [cast/play] [this card] . . . ,” “You can’t [cast/play] [this card] . . . ,” and “[Cast/Play] [this card] only . . . .”
- 604.7. Unlike spells and other kinds of abilities, static abilities can’t use an object’s last known information for purposes of determining how their effects are applied.