It's very easy to fall into the "I know my role, and that's all I need to know" trap. I do it a lot. I could tell you the role of a healer in any non-heroic (and most heroic) ICC 25/10 fights, where they should stand, and what mechanics they have to worry about. But up until recently, the DPS and tanks were a mystery. I knew you needed 2-3 tanks depending on fight, and about an even smattering of melee and ranged.
Well, it's not your job, Bell. Why do you care what they have to do?
To be honest, it is a healer's job to know what the other roles have to deal with. Please notice, I said know, not micromanage. Keep that in mind.
It was once said to me by the Paladin Sharlet: "Good tanks make great healers; good healers make mediocre tanks." Though you can debate it until you're blue in the face, the fact is that healers who understand tanks and their mechanics are better at their jobs than healers who react to damage whack-a-mole style or blinder-zoom on their raid frames. Do you know when your tanks have to routinely pop cooldowns? I am not talking about dangerous, near-death experiences, I'm talking about boss fights in which they need a regular cooldown rotation.
Yes, I am a mediocre tank. I admit it; I tried it on Bellbell and I was just semi-competent in heroics. However, to compensate for that, I've started paying much more attention to boss abilities and cooldowns, understanding when a good tank pops cooldowns and when a mediocre or bad tank would forget to. ToC 25 is a snoozefest for many people in this game, yet on Bellwether my anxiety can shoot up if the PUG DPS is slow and the PUG tanks don't know how to use their cooldowns. That is responsible for more phase 1 tank deaths than shoddy healing, though if a healer with a cooldown had used it, it could have covered for the tank's forgetfulness.
I have never tanked ICC, but I know that tanks need to cycle cooldowns through Festergut's triple stack buff.
Knowing when the melee is all going to get hit, or understanding mechanics like Sindragosa's stacking debuff, can only help you pre-HoT or anticipate health loss for a quick chunk. Is Healbot or Grid set up to tell you who has Unchained Magic so you can pre-HoT them in preparation for the chunk of life disappearing?
It seems like pretty average stuff. Life goes down, I heal it up. Why do I need to know more? As the fights become more involved, as the battles get harder, you will need to know who is standing where, who is heading in what direction, and when tanks are powering through cooldowns so you are able to compensate.
After all, this is, in essence, no different than timing your HoTs to boss mechanics. It is understanding on a deeper level, however, than just "damage happens now." It is "damage happens now and I understand why, so I already have the best possible spell ready."
Again, I'm not telling you to micromanage everyone. Do not be a backseat raider. Just be a smarter healer!