Stance dancing means switching between stances to use abilities which are not normally used in your stance. For example a fury warrior (who would normally fight in zerker stance) might wish to use rend (only useable in battle and defensive stances). It is not an easy skill - you need to be able to switch stances, select the new ability, then shift back to your normal stance very quickly. Spending too long switching means a dps loss, and you need to factor in that when you change stances you lose most of your rage.
Stance dancing, while being something the developers say they like as a flavour of the warrior class, is slowly being phased out of the game. Prot warriors no longer need to stance dance to use charge or intercept, and the latest beta build makes pummel useable in battle stance so assuming this makes it to live arms warriors will not need to dance to access their interrupt. Dancing is critical for PvP, but is a neglected skill for PvE. Here are some abilities which a prot warrior needs to stance dance to use:
This is a fantastic AoE tanking tool which is criminally underused. For the next 12 seconds any attacker hitting you is treated to a mainhand attack in return, with 20 attacks maximum. On a 4 minute cooldown (with the improved disciplines talent) and useable in battle stance only.
I normally (umm honesty attack incoming, let's say - "normally when I remember") hit retaliation before I charge into a large AoE pull, so the button sequence is
battle stance -> retaliation -> defensive stance -> charge -> thunderclap
You can put out a large amount of AoE damage and threat in such situations. Similarly, if you use it just before hitting Challenging Shout you are very unlikely to lose aggro on any mobs within range.
This ability is more useful in single target situations. It makes your next three special attacks crit (not including heroic throw I believe), but at the cost of increasing damage taken by 20% until your three crits have taken place. Again, a 4 minute cooldown (with the improved disciplines talent) and useable in zerker stance only.
The +20% damage taken is scary at first glance, and puts people off, but bear in mind that the debuff only lasts until you have crit three times (about 5 seconds), and you might only expect to take 2 or 3 boss hits in that time. Add to the fact that if you use it on the pull you will probably be pre-hotted and pre-shielded, or with a prayer of mending on you. You will also have shield block available so you can use that to mitigate the extra damage you'll take from using this ability. I believe that shield wall has a shared 12 second cooldown with recklessness and retaliation, so you cannot use shield wall at the same time as recklessness to mitigate the extra damage, but I could be wrong on this. I still think the extra damage shouldn't be a problem though.
Three crits in a row means that your first shield slam will be huge, and you should also be able to get shockwave and revenge crits too. This will give you a very large initial threat lead on a boss.
It's not that well known (it certainly isn't on the tooltip), but this ability also makes you immune to fear. An interesting point that is almost completely useless for prot warriors since when feared you won't be able to shift to zerker stance to use it but nevertheless may come in handy if you are fury spec sometime.
3) Shattering throw
The armour reduction from shattering throw is in addition to the armour reduction from sunder armour. This makes shattering throw a valuable dps cooldown for your raid. Use it during heroism to make yourself very popular with dps warriors, rogues and hunters.
Since it has a cast time, your avoidance will be zero during the cast so you'll take more damage than normal for a couple of seconds but this should only be for one hit given the short casting time and so I don't think that this is a particularly important feature.
4) When not tanking
If you are in a tank swap fight then one of the deadly sins of tanking (ooooh - idea for a blog post!) is to overaggro your fellow tank when it's his or her turn to tank. Generally, Something Bad happens when you do this, at the very least your tanking partner and your healers will know you're a muppet.
Simply shift to battle stance or zerker stance when you aren't tanking to increase the damage you are doing, but reduce the threat of your attacks and reduce the chances of you accidentally overaggroing. This is particularly important for Festergut, since otherwise the massive dps boost you get when offtanking will lead to huge aggro problems for you. Helpfully, it will be easier to get to shattering throw or recklessness during this time, but remember to plan ahead and be ready to shift back to defensive stance well before you need to taunt the boss back.