Really good guide on Healing Basics
Explains the reasoning behind using healing assignments in Sect. 5.2
Much of this I learned healing in EQ where healing chains were used because over healing=wipe every time. Raiding in a hardcore guild which didn't use assignments drove me crazy because of the amount of wasted mana with multiple healers healing the same person and in hard modes this always came down to healers being OOM before fight is over. Any fight in WoW which would be designated a "healer check" or "healer test" is going to require *smart* healing until you simply out-gear the fight.
This guide won't tell you what spells to use or what class is best at what or what your HPS should be. It is a primer for any healer looking to be exceptional and keeping your raid alive through the tough fights.