An action set delay acts like a cooldown for the action set. When the value is 0, the AI will keep trying to use that set, whenever its condition is met. For example, if you have an action set set to "Always True" and a delay of 0, the AI will use whatever ability is in that action set, until you are out of resources. However, if you set that delay to 10 seconds, it will use the ability and then skip over that action set for the next 10 seconds, even if its conditionals are met.
In your picture you used "Not Has Inspiration - Dexterity" to stop it from casting Lightning Strikes non-stop (since it applies a dexterity affliction), but you could have also set it up with something like "Enemies in Melee Range > 0" and put an action set delay to prevent it from repeatedly using the ability every time you are in melee with an enemy.
Hope that helps!