Focuses more on AOE healing through Renewing Mist and Uplift. Imagine if you took the hots of a Druid and the Holy Power of a Paladin and put them in one class. Revival, Chi Torpedo, Life Cocoon are all great as well. It is a bit tough to spot heal sometimes, thanks to how Renewing Mist works, but you can let other healers deal with that, or Soothing does the job well enough.
In PVP, you don't tank damage like other healers quite as much - your key to survival is mobility (and Healing Spheres). You get a lot of fun melee utility abilities as a healer which is kind of nifty - a disarm, a hamstring, Ring of Peace, etc, etc.
You get fistweaving, which can be fairly powerful in PVP, especially if someone isn't expecting the healer they're tunneling to turn around and punch them in the face. In PVE, fistweaving is only used rarely, basically whenever you care more about your DPS than your healing. Its fun, but don't expect Atonement level of cheesiness.
Did I mention Atonement? Spam all the Smites and lol at the meters. If the damage going out is low to medium, or you are between cooldowns and POH doesn't make sense, use Atonement. Its incredibly overpowered even with the recent nerf.
Discipline is great because it is so flexible (unlike that non-Discipline Priest healing specialization). Otherwise, its all about the Spirit Shell and predicting damage. That and Penance makes you a pretty good tank healer. POH is still strong, so don't think your AOE healing is weak, not by a long shot.
The only real drawback to Discipline is also its biggest advantage: absorbs. Absorbs are incredibly op once you get used to them. Absorbs are great for damage you can predict - the best thing out there, in fact. However, if damage going out is greater than your absorbs, Disc isn't so hot at actually filling the green bars once the damage has gone out. Don't stop healing, of course - just Disc does particularly well with a strong throughput healer to back it up.
I haven't done much Disc PVP this xpac - but here's generally the way it works: some guy at Blizzard thinks "Priest" means "Fairy Princess" which means "I need a HERO to RESCUE ME". Disc PVP tends to be about tanking all the damage and hoping/praying your teammates peel for you. That's less the case now that we have Phantasm and the Tier 15 talents, but that's generally how it goes - learn to love your pillar. Disc doesn't have the escapes and immunities of other healers, in general, basically. If someone doesn't actually focus you, you can also put out pretty decent damage (that's part of what has made RMP so strong in arena all these years).