Not many changes are involved to the healing specs and for good reason as well. They simply do not require tweaking. Healing priests are, for the moment, in a sweet niche where they are a joy to play and not in a bad habit to outshine their peers. However, shadow priests are getting a lot of buffs on this one. I do not personally play much on shadow, except when leveling but for me, the changes are quite welcome.
First of all, Vampiric Embrace is turned into the spell that it should always have been; a personal buff on the priest instead of a debuff on the monster that it is now. I cannot image what was going through a designer's mind when that spell was first conceived, but for me I always felt like wasting copious amounts of mana, having to apply it on every mob between pulls.
Now, with this change, shadow priests can join warlocks in large mob pulls, with dots and healing mechanics to compensate, speeding up our game considerably. Sure, we could pull lots of mobs before, but you had to first apply Vampiric Embrace on one of them and then actually avoid killing it, in order to gain healing from the damage you make. To make it further annoying, you had to apply it again on the next pull, spending awful amount of for nothing.
Next up, the Improved Devouring Plague spell will gain an increase of damage, to 10/20/30% per rank, instead of the old 5/10/15%. Not having raided as a shadow priest, I am unsure if this is actually necessary but if the Blizzard wants to throw a damage buff my way, heck I am not going to complain.
Also, Mind Flay is having its range increased, up to 30 yards. Wooah!
Changes to Shadowform are close to my heart in particular, as a priest who is still, in fact, leveling. Not only Devouring Plague, Shadow Word: Pain, and Vampiric Touch benefiting from haste, mana cost for changing forms is dropping from 32% to 13% of base mana. Along with Vampiric Embrace, casting a quick heal on myself during a big trash pull has to be the single-main reason why I oom quickly.
So to sum up these changes; I do not see any major, big changes to the priest play style or damage output. A small nudge to our damage yes, but mainly I see these as welcome changes that will streamline our game a lot. They will lower down time and the class simply just more efficient, as it should be, if go about and compare to e.g. warlocks, our closest compatriots as dotters.