Mobility
I don't know if this is just me, but having the freedom to move around as much as possible at an insane speed is something that keeps this class fun.
I wanted to mention Mobility first because their use of it is unlike any other class. Of course you have your blinks, shadow steps and heroic leaps, but they don't have flying serpent kicks and rolls now do they!
Blizzard did an incredible job with the monk’s mobility because none of them need a target or a spot to be located before you use the spell; this gives the class a unique fluidity that every other class lacks.
Uniqueness
Monks are naturally compared to rogues and druids, each class uses energy as a resource, but monks have another resource to maintain and that's chi. No matter what spec you're playing in, chi is vital in all of the play styles.
As a Windwalker (dps) it gives you a reason to use energy to gain chi, to then be used on killing blows, it's far from clunky and is one of the most fluid specs I have played.
It gives us something else to use and not just tunnel vision the energy bar like other classes, or watch our rage when in tanking form, monks retain their energy and chi even while in Brewmaster (tank) that allows your to use brews and insane absorbs to reduce the amount of punishment your raid takes.
Something I think blizzard implemented perfectly, keeping the class unique and refreshing. Mistweavers (Healer) also gain the use of Chi, making the balance between mana usage and mana regeneration rather unique and keeping your party/raid in perfect harmony of each other and out of harm’s way.
Combat style
As a monk, you won’t feel the need show off your weapon skills so much, instead your animations focus around your punches and kicks, the spell effects are simply great especially the particle density with our aoe spells. Our abilities are clean, and also fluid enough to make the simplest of fights, more entertaining.
There is nothing like doing a ton of back flips in a fight and rolling out of fire! Our stances are awesome too! If you’re a dps, you will be in the stance of the fierce tiger, Stance of the wise serpent if healing is more your thing and then finally Stance of the sturdy Ox while tanking. A nice change from battle/defensive stance.
The specs
Mistweaver - Their ability to spread out heals is incredible although it cannot really be controlled it can be an incredible way to get the whole raid up when needed. Many fights now have predictable damage so using their abilities at specific moments is what makes a good Mistweaver, a better one.
Also they have the greatest healing asset, the ability to move while healing. A mixture of hots and direct healing spells work in perfect harmony together making the monks special mobility great for Mistweavers.
They also have a unique way to regain mana thanks to Mana tea. I hear crit is the best mana regen stat to go for so make use of it!