A Shadowpriest is simply a priest who has placed the majority of his talents into the Shadow tree, and hence has picked up talents along the way that are a staple of any Shadowpriest; Mindflay, Shadowform etc. (Those two spells really make a Shadowpriest [SP for short] stand out)
Also a Shadowpriest specializes his gear to take as much +Spell Damage and +Shadow Damage as possible and some +Spell Hit.
A Shadowpriest can deal a considerable amount of damage as long as they have knowledge of their class and good gear. (I am ALWAYS in at least the top 5 on the damage charts in my guild's Serpentshrine Cavern runs [one of the endgame raids, if you don't know])
One of the Shadowpriest's main benefits are its utility to parties. The two spells I am talking about are Vampiric Embrace and Vampiric Touch.
Vampiric Embrace (with improved VE) returns 25% of your Shadow Damage in health to the WHOLE party. Vampiric Touch, as well as being a powerful Damage over Time spell, returns 5% of your Shadow Damage in mana to the WHOLE party.
These two spells make Shadowpriests both a very desirable class and a unique class.
To conclude, a Shadowpriest is essentially, a lean, mean, fightin' machine that is a mana and health battery and, to top it all off, glows purple!
Read the SP FAQ at the top of this page, as well as Khalane's SP PvE guide a few posts down to get some much more in depth insight into the class.
Also, a good resource is shadowpriest.com, although a lot of that information is for SP's who are rading or already have a thorough understanding of the class.
Feel free to Private Message me if you want some more specific questions answered.
Edited, Nov 26th 2007 1:26am by Schmere
Edited, Nov 26th 2007 1:27am by Schmere