If there's one factor that I've come to realize separates most veteran healers I know from those who can't heal or are just learning to heal it is this crucial skill.
Perhaps this skill has enscorceled itself in my mind due to the very proactive nature of Druid healing, but I believe it was reinforced greatly by my time spent raiding as a Hunter.
As a raiding DPS class, your responsibility is to pump as much sustainable damage into a target as possible without passing the tank or ignoring your surroundings. In order to accomplish this goal, most classes have a set rotation (or a priority, calm down Rilgon) of skills that have been mathematically shown to maximize damage output when chained together in the most efficient manner possible. You train yourself to fill every GCD with the most efficient action available to you (much lik the queue systems in games like BioWare's first two KOTOR game, without the queue :P). If you're the type that likes to compete the top spots on a damage meter, then the phrase "balls to the wall" becomes a part of your vernacular and, when circumstances fall into place, becomes your default setting until the boss lies before you unmoving or you're poking of pile of Obi-Wan-esque disembodied clothing.
In contrast, the majority of healers that I meet view healing as a purely reactive exercise: when someone needs a heal, then I'll press a button.
This type of mindest can serve you well in a large portion of the game, from leveling to even most Heroics. Some raid fights can even be approached this way if the rest of your group is executing with perfection.
The point where this approach to healing falls apart is when the fecal matter strikes the proverbial fan.
Healers who want to bring their A game and be remembered as that "crazy good priest that saved our bacon even after the tank's mouse broke" should train themselves to approach healing more in the same manner as DPS. The healers that stick out in people's minds like that are likely a druid that keeps Wild Growth up even if the melee is at full health just in case he needs to drop a quick Nourish on a Rogue who mistakenly walks through a poison cloud, a paladin that has the Death Knight who can't dodge Dark Smash beaconed without complaining and without the group realizing it, or a priest who tosses up a Lightwell for his own personal use so that his GCDs are free for the rest of his healing assignments.
I know what you're thinking. "But Ani, if I push through every single GCD, I'll run myself out of mana!!".
I'll admit it.
I'm biased in this regard, likely because I've always had the "crutch" of Innervate to fall back on when I get overzealous. Knowing the line between maximizing throughput and running yourself dry is an acquired skill that differs with the mechanics of the fight you're facing. On progression content this can be particularly challenging, but that's mainly because the amount of unnecessary healing that learning fights results in.
But! Unnecessary healing is where the truly good healers shine through. They're on their toes, being preemptive and pulling their groups back from the snatching jaws of the raid leader calling "Wipe it up." I'm not asking you to encourage apathy on the part of your raid when it comes to avoiding the avoidable; nor am I asking you to reward that (healing through the mistake) without communicating your displeasure afterwords. I'm encouraging you to view every single Global Cooldown you have as just as valuable as the ones I can assure you your DPS aren't wasting.
Every space between your cast times has an opportunity cost: evaluate it, assess whether you need to keep healing in order to best serve your raid or back up to conserve mana, but always be mindful of what ability could have been used and the difference it could have made.
Your resources may be more finite than their resources (always be aware of the limitations of your mana pool), but your contribution is just as vital and FAR MORE dependent upon your ability to adapt quickly to what happens.
Waiting for a reason to heal is just going to result in you getting behind and someone's going to end up falling through the cracks.