Focus is a gauge above the Stamina gauge that modifies your weapon's attack when activated. To obtain Focus, finesse actions are required (like dodging a moment before an attack hits), though taking large damage from an attack can also contribute to your Focus build-up.
While under the effects of Focus, your Stamina is immediately replenished. You become more resistant to stagger, and your attacks are more likely to stagger the enemy. Various passive skills also take effect only while under Focus, and others can contribute to how quickly it builds up. While under the effects of Focus, you can also press your [Run] + [Heavy Attack] buttons to deliver a launch attack for massive damage and a great Ichor bonus.
Enemies also have Focus gauge (unconfirmed for bosses), which can result in uncertain behaviors when fighting them.