Outer demons are anything that we relate to with attachment or aversion. Any material objects, forms, sounds, tastes or physical sensations that we experience getting ourselves caught up in. We get hooked by our fixation which creates the conditions for bondage and suffering, which is why they are called 'demons'. They are called 'outer' because they are objects of the five sense faculties.
We should strive to cut-through these demons, strive to eliminate their influence and our habit of falling under their power. We cannot stop them from appearing, but we can cut through our fixation on them as being real and permanent. We can look through their outer appearance and see their true nature.
Eliminate grasping and they are powerless. You are liberated.
Inner demons are concepts that bring your fear and terror. They haunt you at night and torment you ceaselessly. Grasping at these good and bad thoughts causes the mind to become afflicted with negative emotions, bringing you great harm and causing you to act out like a fool, thus they are 'demons'. They are 'inner' because they are the experience of your mind and mental states, a world of experience that you get wrapped up in and struggle to escape.
We should strive to cut-through these demons. We don't need to block thoughts or memories, but also don't hold onto them and dwell on them. Recognize their true nature to be like waves on the water, rising and falling but leaving without a trace. Relax into your own true nature and the disturbances naturally subside, liberated in their own place.
Demon of Elation
The demon of elation is the result of mental attachment to delight and joy. This could be the result of some worldly gain, fame, accomplishment, some great experience you had or some sign of success. They are called 'demons' because they cause great arrogance and pride in oneself which becomes an obstacles to freedom.
We should strive to cut-through this demon. Whenever good things happen, don't fixate on the qualities of that experience. Recognize them as being like a dream or illusion. It is possible to enjoy experience free from fixation and grasping, as you integrate your experience with the path and achieve success in cutting-through the demon of elation, you will truly be able to extend yourself and benefit others.
Demon of Self-Importance
The demon of self-importance is the root of all demons. This demon arises from the self-grasping that is the root of all suffering and dissatisfaction. It is the chronic disease that blocks the attainment of freedom and awakening.
We should strive to cut-through this fixation on 'I' and 'mine'. Cut-through to our true nature, our buddhanature, our originally pure and spontaneously present nature of mind.
Where there is ego, there is also a demon. Where there is no ego, no demon can be found.
Ephemeral- without mental designations.
Mind free and easy- fixation on 'I' annihilated.
Pristine- incapable of disturbance by emotional conditions.
Clear- consciousness free of outer and inner duality.
Transparent- awareness free of attachment to anything whatsoever.