What does it mean to be healable?

It means different things at different levels of the game. I’ll be focusing on ten and twenty-five man raids.

In general, being healable is defined as the ability to survive long enough against monsters that your healers can keep you alive. If your dead, you can’t hold aggro (save versus the floor). There are a few aspects to help being healable.

1) 490 Defense. This is a must, before stepping into any dungeon. It prevents you, under normal circumstances*, from being critically hit. Crits from monsters are Double damage. They can rapidly take a tank at moderate health down to dangerous levels. When followed by other critical hits, crushing blows, or special abilities, it can result in a dead tank before even the best healers can react. More then 490 defense still increases block/dodge/parry, but it is the least desirable way to obtain any of these. Try to stay as close to 490 defense without going under.

*if a monster mind control’s a druid with Leader of the Pack, or receives some other type of buff that increases their critical hit chance above the base 5%, you can still be crit, (example from Musluk) You can also be Crit if you press a button hotkeyed to /sit, either “X” or “C”, so remove that keybinding
Malicious Instructor in Shadow Labyrinth is also known to crit warrior's with 525 Def, as noted by Satrina of evil empire

2) Shield Block (Skill). When shield block is up, your total avoidance ( parry + block + dodge + miss) is over 100%. This removes crushing blows from the combat table. Crushing Blows are 1.5x Normal Damage. In many cases, constant use of Shield Block, along with the improved shield block talent, can keep you from taking a crushing blow. This is not possible on all bosses, particularly bosses who dual wield (Moroes, Prince Phase 2, ect). Therefore, the focus is on minimizing crushing blows, which allows for a steadier stream of damage. The less spiky the damage you take is, the less the healers have to adjust healing levels. (It is possible to become passively crushing blow immune, if your block + parry + dodge + miss is over 100%, see page four)

Also note the difference between Shield Block Value and Shield Block Rating.
Value increases the amount of damage blocked with each attack, and the damage done by shield slam. This is highly desirable, and should be stacked where reasonably possible.
Shield Block Rating affects how often you block. It is less beneficial when your taking only one or two hits every six seconds (and the shield block skill is making those blocks anyway), and more beneficial when your taking lots of hits (fast hitting boss, multiple monsters, ect).

3) Stamina Stacking. Avoidance (Dodge, Parry) was nice for five mans. You had one healer, that healer could stop a big heal from landing if you had a string of dodges / parries, and no mob was going to bring you down from full HP to dead in the amount of time that you could be healed.

Many bosses have abilities that will hit hard, and fast. Prince thrashes in phase two, potentially landing three hits back-to-back, and no warrior can prevent the chance of the last hit being crushing. Gruul’s hits get bigger and bigger, with normal melee of 8,000-10,000 and hurtful strikes of 16,000+ at high grows possible during a normal kill. Bosses parring attacks can cause damage spikes (parrying an attack increases the speed of your next attack). Going with avoidance is playing a dangerous lottery. There is no guarantee that you will avoid hits. There is no chance that you will be able to be healed through one if your total HP is less then the damage from the hit.

That said, avoidance is still desirable, just not at the cost of stamina (excepting extreme circumstances; I'd give up two stamina for 1% dodge). Having an alternate set of gear for avoidance can be a smart move.

“The focus is not on taking as little damage as possible, but being able to take as much damage as possible” –Ciderhelm.

Some argue that avoidance increases healing mana efficiency. In a ten man, and especially a 25 man, you will be getting healed whether or not you dodge or parry. You aren’t doing anyone any favors by dodging a 5k hit, and getting overhealed for 4k.

Also important: Stamina is affected by Blessing of Kings, and our vitality talent. It scales significantly.

(There is also the (non-) issue of rage generation. I don’t use this as an argument for stacking stamina simply because it’s not necessarily true, and easily attacked / proven wrong. In 25 man raids, you’ll have plenty of rage no matter how much avoidance you have)

4) Communicate with the Healers – Get a mic, and use it. Let them know when you use Last Stand, Shield Wall, ect. If they aren’t familiar with a boss mechanic or one of your abilities, explain it. When a monster heads towards someone that isn’t you, tell them. All of these things direct how and where healing goes, and can be hard for them to track when they are focused on health bars, their mana, ect.

5) Additional Tips - Use your Warrior Offtanks. Have them Intervene you during Silences (Maiden or Gruul, for example) or Enrages (Various Trash). Spreading out the damage is the only "heal" that you will get during a silence. Use your consumables and cooldowns appropriately - during silences, they are your healer.

Resiliance - This is normally a stat to be avoided, as it has no use when you are at 490 Def. However - it can be a valuable stat on a non-conventional fight like Hydross, where you aren't going to be at 490 Def. Aris recommends a S1 or S2 Shield, with the Resil. Enchant on it, as a great way to close the gap to crit immunity.

This observation was taking from a WoWhead user named Yakra.