Poise decides how well you can take a hit without being staggered or knocked down. You do not level it with an attribute; it comes from the armor and talismans you wear and from a few other effects.
Where your Poise comes from
Armor pieces and certain talismans add to it. If you take enough Poise damage within a short window, you are interrupted, so the more Poise you have, the more punishment you can absorb before that happens. For a short burst, the unique skill on the Grafted Blade Greatsword greatly increases Poise for 5 seconds. Since armor adds weight, keep an eye on your Equip Load when chasing Poise.
Enemy Poise and stance breaks
Enemies work with two systems. The first is the same Poise you have: hit them hard enough in a short time and they flinch. The second is stance. Deal enough stance damage quickly and the enemy collapses, opening them up to a critical hit. Their stance meter resets after roughly 8 to 20 seconds, depending on the enemy, but every hit you land restarts that timer, so steady pressure keeps it from refilling.
Mounted enemies such as the Tree Sentinel and Night’s Cavalry are the exception: breaking their stance does not open them up for a critical attack.
Related stats
For staying alive through the hits you cannot shrug off, see HP and Vigor. For blocking instead of tanking, your Stamina matters most.