You are burning, bleeding, covered in acid, afflicted by a wasting curse, or otherwise taking damage over time.
You can only suffer from one instance of the same type of Persistent Damage effect, i.e., if you’re already on fire you can’t be set on fire again to suffer from two instances of Persistent Damage (Fire). You can suffer from more than one instance of Persistent Damage if the effects are of different damage types, however, such as Bleed, Fire, Necrotic, etc.
At the end of your turn, if you are afflicted by a Persistent Damage effect, you take the listed amount of damage, and then make a DC 10 Flat Check to attempt to remove the Persistent Damage effect. If you are suffering from multiple Persistent Damage effects, you take damage from each and make a Flat Check against each independently.
Unless stated otherwise in the ability that inflicts it, Persistent Damage lasts for 1 minute. The creature suffering from it continues to make Flat Checks to end the affliction even if it is Unconscious or otherwise unable to act.
If you spend at least 1 Minor Action on your turn to take an action that would plausibly remove the Persistent Damage effect (splashing yourself with water if you’re on fire, for instance), the GM may grant you Advantage on your Flat Check, or allow you to immediately roll a Flat Check against the effect before it deals damage. Note that some kinds of Persistent Damage can be automatically removed by specific actions, such as First Aid removing Persistent Damage (Bleed).