True Tri Spec refers to a build that is somewhere close to 21 Shadow (silence), 21 Discipline (inner focus), 9 Holy (Spiritual Healing and Renew).  This build is a good general build, taking some of the advantages of the three trees.  Unfortunately, by not digging deep into any tree, the priest gives up the capabilities of all 3 trees. I am not overly fond of a standard tri spec.
Here is why:

The damage dealing strength of the shadow tree comes from the bottom 3 rows: Weaving (+15% damage), Darkness (+10% damage) and Shadow form (+15% damage) which results in almost a 50% increase in damage.  By not digging all the way down the shadow tree, the priest becomes only a better damage dealer than a holy priest but not near the caliber of a shadow priest, but still suffers from the awful inefficiencies of the shadow tree's spells.
The tri spec gleans the percentage based holy abilities so he looks on par on paper. Unfortunately, the priest looses all the utility and survivability abilities of the lower holy tree.  This makes him a slightly better healer than a Shadow Priest, but not on par with a Holy or most Discipline Priest.  For example, he does not gain Improved Prayer of Healing, Improved Flash Heal, Subtelty or Inspiration.
Though a tri spec priest will dig deep into the discipline tree, they will miss the ability that makes the tree: meditation. Without meditation to regenerate mana, and master healer (from the holy tree) to improve Greater Heal, the priest does not have the staying power of other priests and is constantly under the 5 second rule.
Overall, the tri-spec priest does have a tremendous amount of utility, though I personally do not care for it. The can solo to a certain extent, unlike the holy/disc builds, and are reasonably effective in PvP, they just aren't really good at anything.
<h3><a name = "ShadowHoly">Shadow w/Holy + Disc</a>
This unique build was created by Tristfall of Obsidian Guild on the Lightning’s Blade server and is IMHO one of the better builds available to those that want to solo and compete in the high end instances.  This build takes shadow down to the Shadow Form (thus ensuring soloing capability), then splits the remaining 20 points between holy and disc, as opposed to just discipline.

The advantage of this build is that the priest is still a competent damage dealer but has improved healing abilities.

Unfortunately there are a number of disadvantages to this build, similar to those of the Tri Spec and the pure Shadow/Disc end game build. The priest lacks the efficiency gleaned from the Discipline tree and the utility from the Holy tree. The priest also lacks the bonus 10% mana from Mental Strength and the mana bar lengthening of Agility.

Still, the priest can solo and does have fairly decent healing abilities.
<br><b>Example Build</b><br>
Discipline Talents (21 points)

Unbreakable Will - 5/5 points
Improved Power Word: Shield - 3/3 points
Improved Power Word: Fortitude - 2/2 points
Mental Agility - 5/5 points
Mental Strength - 5/5 points
Inner Focus - 1/1 point

Holy Talents (9 points)

Improved Renew - 5/5 points
Spiritual Healing - 4/5 points

Shadow Talents (21 points)

Blackout - 5/5 points
Shadow Focus - 5/5 points
Improved Shadow Word: Pain - 2/2 points
Mind Flay - 1/1 point
Improved Psychic Scream - 2/2 points
Improved Mind Blast - 2/5 points
Shadow Reach - 3/3 points
Silence - 1/1 point