With the update of the talent trees for wrath, Blizzard have created two very distinct paths for priest healing.
Until now, a healer's job has been to heal damage. Healing talents have been those that maximise healing output or efficiency. Gearing a healer has been about either making a heal bigger, or allowing more heals to be cast, both of which have the overall effect of making the total amount of damage healed go up. The "skill" of a healer has been making this healing count, by timing to avoid overheals, etc.
Discipline priests have a different goal: to make the amount of healing they do go down!
Here's a sample Disc build:
http://www.wowhead.com/?talent=bVcbuhxtMx0ifMt0xxcThe remaining 3 points could be put in the 1-pointers (Desperate Prayer, Power Infusion, Pain Suppression) or Absolution, depending on whether you prefer loads of situational buttons or better core efficiency.
A discipline priest lacks the talents in the holy tree that boost the size of big heals, and instead has talents that synergise to reduce the amount of damage taken in the first place, and do this with incredible efficiency.
The keystone talent is Rapture, which returns mana based on not only the amount healed, but also the amount absorbed by shields (including Divine Aegis procs!). This scales with int and crit, and lies at the heart of a disc preist's efficiency.
Grace reduces all damage taken
Inspiration reduces physical damage by bosting armour. Scales with crit.
PW:S absorbs incoming damage (also gives 25% haste for next spell, and the weakened soul debuf boosts crit by 4%)
Divine Aegis absorbs incoming damage. Scales with crit
Notice how a particular word keeps cropping up? The best stat for disc priests is crit! Closely followed by int (which also boosts crit!) which disc gets at +15% (thanks to Mental Strength), then spellpower, then haste (we already get +5%, often boosted by an additional +25%!) and mp5.
The old key priest stat, spirit, is very low on the list. Disc healing is about lots of small casts, so we get almost no time outside the 5 second rule. We also don't get the conversion of spirit to spellpower that holy priests do. The only thing spirit does is add to mana-regen via meditation. Disc priests will likely get enough spirit by accident - no point choosing to gear for it.
The style of play is much more fast and furious than holy spec, and works well for "reactive" healers. No more /stopcasting greater heals, instead it uses instants (PW:S, PoM), and the instantly responsive Penance.
For boss fights, typically Penance, PoM and PW;S should all be used on cooldown on the tank (focus target is your friend), with the gaps in the penance rotation used for FH, GH, HN, PoH (or PW:S on another raid member)
Via Rapture, a PW:S (that gets used) is almost mana-free and gives a ton of synergy via Borrowed Time and Renewed Hope (tip: For emergency healing a lot of damage, cast PW;S, Rapture, then Greater Heal. Rapture will not consume the haste from Borrowed Time, making the GH very quick indeed!)
Only use renew for life-tapping warlocks or if you're bored. With the amount of haste we get, a flash heal fits comfortably within the same GCD, heals for the same amount (but all up front!) and has a chance to proc DA and Inspiration, as well as return more mana from Rapture.
Instead of Circle of Healing, a glyphed Holy Nova works very well, and surprisingly efficiently, though is obviously limited by group (not raid wide). (tip: During aggro-drops when you're at risk of pulling, use PoM - at the moment it's not generating aggro - and run about like an idiot casting Holy Nova - it's also aggro free! It's times like this you'll be happy you didn't have renew on anyone). An Inner Focus/PoH combo will give a free, bigger heal and also trigger Divine Aegis on most of the group.
I see Holy spec keeping it's place as the preferred build in 25 man raids, but for 10 man and heroics I think disc has the potential to really shine.
As a last point, I'd like to recommend Grid to any healer who hasn't already tried it (are there any of those left?