It’s a complicated issue, really.
Healing isn’t so simple that there’s always one solution. As a DPS or a tank, you do the same thing over and over and it never changes outside of RNG giving you a lucky crit or proc.
As a healer, though, you have to adapt to the other healers’ capabilities and your raid’s incoming damage.
As a Priest, you’re uniquely equipped to heal people “reactively” with Flash Heal, just slightly faster than a Paladin’s Flash of Light if you have 3/8 T1, otherwise equal. However, reactive healing generally produces poor results no matter what class you play. The best way to improve your healing is to learn to play proactively.
What that means is essentially always being aware of the damage people are going to take, rather than the damage they already have. When playing reactively, you’re noticing a health bar isn’t full, then casting a heal on them. This can be improved with mouseover macros or add-ons, practicing reaction times, etc, but is ultimately limited by your cast speed + your reaction.
By contrast, proactive healing involves casting the heal before the damage is taken, so the cast finishes immediately after. This is easiest to perform on dragon fights with the breath abilities like Shadow Flame and Breath of Fire. Simply charge up a bigger, slower heal on a target that is about to take lots of damage.
On Firemaw, for example, there is lots of proactive healing you can do. If you are particularly skilled, you can time Renew ticks with the tick of Flame Buffet, or a Flash Heal. You can use the easy method of just using Power Word: Shield to prevent the damage in the first place, as long as you know that damage will actually be taken (though this isn’t very mana efficient or high HPS). You can also charge a Greater Heal when you know a breath is being cast on the tank.
There’s only three bosses that come to my mind: Lucifron, Baron Geddon, and Chromaggus.
For Lucifron, your raid should use Restorative Potions and you shouldn’t need to dispel anything aside from Mind Control.
For Baron Geddon, there’s very little healing that needs to be done in the first place, so you should be content to just dispel spam away. If your guild has healing assignments, you can save some mana by only having to dispel 5 people before going back to healing.
For Chromaggus, there are usually two dedicated dispellers, and one will be a Paladin, while the other is a Druid. If you’re Horde, there’s probably something you’ll have to do as a Priest, Shamans are using Totems, and the Druid decurses as normal. For that, if you’re assigned to dispel, you ONLY dispel. Otherwise, you only heal. It’s fairly easy.