Poise is a game mechanic in Dark Souls III.
Poise currently has two different effects in Dark Souls III. Items with a poise stat will raise your poise stat as expected. Skills that describe a temporary boost to poise do something entirely different.
The Poise Stat Edit
Your total poise on your character page affects how much Poise damage your character can receive before being staggered out of any Hyper Armor animation. Poise does not affect staggers in any way outside of enhancing your Hyper Armors.
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 gets staggered and will get knocked out of the animation.
Getting staggered due to Poise Bar depletion will reset your Poise back to 100%. Not receiving damage for 30 seconds also 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.