My interpretation (or simply what I like to believe) regarding priests:
In the universe there is something, or there is nothing at all. There is energy, light, matter, or there is not. There is the Light or there is the Void, and all living beings, as being born of the light, are unable to view the Void, as in the act of viewing it, it causes it to exist, which it does not.
Priests in WoW are energy manipulators, something akin in the manner of an arcanist, yet they use sheer inner strength and belief of their understanding to make it happen in a manner of mind over matter. Rather than channelling magics they are capable of manipulating their own energies to influence the bodies of others. They view how the light warms the morning, causes the plants to grow; they force their very essence to mimic that force on a tiny scale to accomplish what they see as the will of the light. To create, and heal. They do not require runes or symbols - they require only the knowledge and the strength of will to force it to happen from the depths of their souls. This applies to both Holy and Shadow priests in different ways. Tenacity - the sun will shine each day despite what evils befall Azeroth, and with its mimicry, a true priest will apply such determination and unwavering strength to persist until their goals are done. Respect - to understand and respect the light's ability is key. The light is a burning fire of energy - one that can be used to destroy or to create. Compassion - those of the holy light choose to manipulate its existence to spread peace and compassion - to protect and to heal, to bring joy.
Despite being a shadow tenet, power is key to a priest. Light is the power. Their soul is the power. Knowledge is the power. Note how a priest's spells do not refer to light - they are wielding it for other purposes, not using it directly:
A priest will cast: Penance, Serenity, Sanctuary, Heal, Flash Heal, Binding Heal, Prayer of Healing.
A paladin will cast: Divine Light, Holy Light, Flash of Light, Holy Radiance, Light of Dawn.
You can tell from this that paladin will channel the light and throw it around with good intentions, but little understanding. They channel it and hope and have faith that it will do what they want - a priest requires no such imprecise work. They use the light, yes, but as a power source to do as they please and will to happen, and that is the difference between them.
So what then? Is a shadow priest? What is it they do? Where do they draw their power from?
As Yva has decribed many times, I believe that all priests in some way or another begin on the holy side of the coin. They spend their years meditating on the nature of the soul, of desire, of will and of the universe. Like any other bunch of aspiring priests, only a few will come to the true comprehension of the strength of will. Of those, a few will come to question "If the light is everything around us - imbued in every molecule of life - then what is its absence?" "I use the light within myself and expel it with my will to others to assist them in their hours of needs - what if I took it from them by force?" Most priests will be terrified of the thought and shy away from such a horrific notion, but others will not. Others will be curious, because they understand the power within themselves - but what if they could have everyone else's too?
A shadow priest becomes familiar with The Void. WoW Lore states the The Great Dark Beyond as the "space between worlds" and personally I don't buy some of this wishy-washy world and universe talk; I've decided to read between the lines myself. In my interpretation The Void, The Great Dark Beyond are a singular thing, and it is indeed the space between worlds, as it is the last vestiges of the vast nothingness that existed before the universe exploded into existence. Before the creation of light, energy, matter and time there was the void; a vast gnawing nothingness that spanned to eternity and infinity, yet did not. A paradox that we cannot quite understand with our human minds, attuned to the laws of physics in our own universe. Now, there is light, energy and matter everywhere. It is chaotic and it creates - it permeates to the deepest parts of interstellar space - photons whizzing through space. However, in the space between worlds - there are large areas of nothingness. Where not a photon passes, and there is only vaccum. There is nothingness. In these spaces, reflected in the viewing of a black hole (though I am aware that a black hole does indeed have mass and energy), there appears to be nothing, but an infinite maw. This is where a shadow priest draws their power from.
I don't like the idea that shadow priests "draw" power from anything but themselves, nor that priests in general do. I like to believe that all power comes from themselves, and they use the framework of an idea or a thought as a pattern for their power. A shadow priest has come to understand the nature of nothingness and in the process the void. The Void is not meant to be seen, as I pointed out above, but shadow priests through sheer desire have come to comprehend a mere fraction of its power - the power of a supermassive black hole, and how it could swallow up a universe. Such knowledge would drive most insane - again reducing the number of potential shadow priests, and yet a small few, are capable of maintaining their mind with such ken, which changes them forever.
A shadow priest realises that the void has the capacity to destroy entire universes and create them - it is the ultimate god-like power - and they want it for themselves. While a holy priest emulates the sun, they emulate the black hole. Sucking in the life and light around them - forcibly stealing the light from others and using it to fuel their own power. I believe that the "mind" and "insanity" aspect of crippling their foes is very simple - they are a shadow of the void themselves, and their mere existence in such a form is enough to drive lesser minds into the ground. "Mind blast" "Mind Flay" "Mind Spike" "Insanity" are not glowing beams of mind-stuff - but interpretations of how they expose the weakened psyche of their foe to what they are, what they have become and what they know.
A shadow priest does not need anything to kill you. It need you to know about nothingness, and watch you slowly kill yourself as you fail to cope with the comprehension.
This is really poorly written as I've not had enough coffee yet, but it's the jist of my thoughts on the matter.