IIEE has to do with the phases of action within resolution, both with respect to real world actions taken by the players and imaginary events affecting the charracters. For example, when one rolls to see if a character strikes a target with an arrow this is often thought of as one discrete action, but it is helpful to break it down further into parts to see exactly how the effect is arrived at. So:
Intent: "The player announces the intended action for the character. No movement or action has happened yet, though. The intention and its consequences may be discussed among the GM and players and changed. "
So, for the archery example, Intent would be when the player first says "I want to have my character shoot that apple with an arrow".
Initiation: "The player has committed his character to the task, and no changes can be made now. The dice hit the table. "
The player consults the GM, looks at the appropriate stats and takes out the dice to roll. The mechanical process has been initiated. In the imaginary events, the character commences on the actions.
Execution: "The character completes his action. The player looks to see how well the character did."
The dice are rolled in the real world. The arrow is shot in the SIS.
Effect: "The players and GM decide what the effect of the task is, whether successfully completed or not."
Based on the values rolled on the dice, an outcome is decided upon. In the game world, the arrow hits or misses the apple appropriately.
Each step can be handled differently depending on the rules of the game, but accounting explicitly for each step in some way is needed for the rules to be complete.