Basically, when tanks are gearing they can choose to stack stamina or avoidance stats like dodge/parry/mastery/(crit too for druid only).
Avoidance lowers incoming damage but involves a little bit of RNG (even at very high avoidance values, yes, still a bit of RNG). But against an avoidance stacked tank your newly level 85 priest will feel much more comfortable because taking less damage means your gheal being fairly small, doesn't make it feel inadequate
At some point though when healers are geared AND the tank has high enough avoidance, some tanks start to prefer more health, trading dodge/block/parry to make their healthpool big. Sadly that means if you're undergeared you can't keep up with the damage they'll take, but when paired with a geared healer it has its perks. Basically damage patterns are much more predictable on a tank with really high health.