When you go into shadow form, you are pretty much denouncing the happy cheery healing part of the (diety) and going rogue and using your powers to melt faces instead of heal wounds. Its a physical show of how your soul is going to a darker place.

And it looks freaking awesome.

No lore reason, as far as I know. It's just a game mechanic to help balancing specs similar to Druid forms. Kitty's get knocked out of Cat form for casting healing spells so they don't spend they're time waiting for Energy by spamming Lifebloom on themselves, likewise SPriests having a "stance" in which they can't cast healing spells keeps them from being -too- versatile.

What I've always heard is that Shadowform is a graphical representation of the player nearly reaching the pinnacle of the Forgotten Shadow's philosophy, that of Ascension, wherein the priest becomes an immortal creature of shadow. Players are able to tap into a lesser version of this, as truly immortal characters would be a little difficult to balance.

http://www.wowpedia.org/Forgotten_Shadow#Ascension

@ilmyrn: "....truly immortal characters would be a little difficult to balance...."
Because character aging penalties play such a big part of the game today?

"The ultimate goal of practitioners of the Forgotten Shadow is to ascend. Ascension occurs once a person achieves complete control over herself and the power to transcend death. A Forsaken who ascends becomes invulnerable, invincible and eternal. In essence, he becomes a god. "

Its 100% lore-related. A shadow priest aspires to leave its body and become a spirit. Dispersion is that ultimate form, Shadow Form is on the road, but not quite there. This lore is the reason dispersion is the ultimate talent, as it is the ultimate achievement in the shadow cult.

Styopa is pointing out that immortal and invincible are different things. The Draenei are truly immortal; they do not die of old age. Yet they're not invincible, you can kill them, unless they're paladins during divine protection.