Poise is a game mechanic in Dark Souls III.
Poise does not work as it did in the previous games. In the previous games there were what is commonly defined as "Passive Poise". The active effect of poise is now defined Hyper Armor.
Poise now works like a wet noodle. It only works if you swing it around, and flops over if you don't hit first.
The Poise Stat Edit
Your character's total poise affects how much Poise damage your character can receive before being staggered out of any Hyper Armor animation. Poise does not affect stagger animations in any way outside of enhancing the performance of the Hyper Armor effect.
The Poise stat increases a hidden Poise Bar (similar to the Stamina Bar, albeit invisible to the player). Receiving Poise damage during Hyper Armor will reduce the Poise Bar, and if it completely depletes, your character becomes staggered and will get knocked out of their animation.
If your character is staggered due to poise bar depletion, it will regenerate over a small period of time. Not receiving damage for 30 seconds resets the Poise Bar back to maximum.
Building high Poise will give you the advantage of winning trades, as you will be able to endure more hits before being staggered and will be able to continue your Hyper Armor animation.
It was initially believed that Poise had no effect in-game, but it actually worked in a totally different way. 
Skills With a Poise Effect Edit
Skills with a temporary poise boost do not increase the player's poise stat. Instead, the temporary effect is to be immune to stagger and thus able to continue casting, moving, or attacking.