Animation cancelling refers to the fact that when you weave an oGCD immediately following a GCD ability with a long animation, the floating combat text (with the damage numbers/debuffs) appears more quickly, rather than at the end of the animation. It's not unique to WAR at all; it was incidentally first taught in BLM circles as the ancient ritual of fireweaving, to check for firestarter procs.
It gained some interest amongst tanks during the final raid tier of A Realm Reborn, when 'snap aggro generation' became a popular subject of discussion, especially as a WAR offtank picking up adds (phase 2 of t13). The third hit of every tank's enmity combo (Rage of Halone/Butcher's Block/Power Slash) has a relatively long animation, with the damage/enmity only occurring at the end. You may have noticed this if you use RoH/BB/PS on a mob just as you lose aggro on it: it wanders off, the animation finishes, and then it wanders back.
The idea at the time was that if you used an oGCD (i.e. Brutal Swing) immediately following BB, the damage/enmity from BB would activate faster, allowing you to secure aggro more quickly, because the damage numbers seemed to be appearing more quickly. The original author of this claim later
retracted it after additional testing.
WAR has a strong mitigation kit with relatively short recasts on its defensive abilities. The flipside is that WAR starts to hemorrhage dps if you put sustained pressure on them, forcing them to become more reliant on Defiance and Inner Beast. Survivability is not an issue for any tank, but different tanks are better suited offensively to tank certain parts of a given fight.
IB's function is a bit odd. With 2.1, it was supposed to be WAR's answer to Rampart. It's availability, however, meant that you could mitigate every significant hit with IB, on top of your other major cooldowns. It's significantly easier to time than Rampart and Shadowskin on single hit tankbusters, as you're often aiming to activate these skills much further in advance than you would IB (i.e. 18-19 seconds in advance instead of 4-5 seconds) in order to cut back on the recast time. HW somewhat addressed this by making Defiance and IB less desirable, through Deliverance and Fell Cleave respectively. RI is functionally more similar to Rampart, with IB now functioning more along the lines of the other tanks' short recast cooldowns (Sheltron/Dark Mind).
DRK isn't about brute force. WAR's attacks are built around big, weighty hits that do large amounts of damage. DRK is about speed and finesse. Between the haste boost of Blood Weapon and the oGCDs, you're forced to quickly prioritise and map out your next actions much further in advance. You have the potential to play at a higher rate of actions per minute than even some melee dps jobs, let alone your co-tanks.
It is extremely rewarding if you enjoy the tactical side of tanking. You'll find yourself asking questions like "Can I position these two mobs close enough that I can hit both of them with Salted Earth, but far enough away from each other that they don't tether?" or "Can I help AoE down that cluster of mobs while tanking the boss in another corner of the room?" or "What sorts of distant destructible objects can I get Soul Survivor procs off of today?"
Gap closers are knockback negation tools, but they're still also gap closers. They increase your melee uptime. The simplest example of this is where you're forced away from a mob because of a point-blank AoE or distance-based mechanic, and you flip back instantly when the game snapshots your position to determine whether you take the hit. There are plenty of places, especially this raid tier, where this can let you squeeze in an extra GCD or two.
Remember, everyone expects WAR to do more damage, partially by reputation and partially because they're designed to at baseline. You gotta play smart if you want to
close the gap.