Biological: This damage is based on creatures having generally mundane biology. Things like poisons, diseases, bleeding, etc., all cause biological damage. Non-biological creatures, such as constructs, are immune to this.
Keyword: Some damage types have a keyword appended to them. For example, “Divine (Unholy) damage” is divine damage with the unholy keyword added on. This often describes the source or more specific nature of the kind of damage.
Non-Lethal: This damage cannot cause death. If non-lethal damage would reduce the target below 0 HP, it instead leaves them at 0 HP and they are knocked out. All damage is considered to be lethal unless otherwise mentioned.
Precision: This is damage that only works if the creature can be critically hit as it is based on delivering an attack in an exact fashion.
Persistent: This is damage that is taken every turn at the end of their turn until some stated point in time (if unlisted it lasts for 3 rounds). Persistent damage ignores Threshold.
Note: Multiple instances of persistent damage don’t stack, the target just takes the highest damage (though still suffers any additional effects from other sources of damage).
Material: This damage was done with certain material. While this usually doesn't provide a benefit by itself, certain creatures may be vulnerable to particular materials. For example, a silver weapon injures werewolves more effectively.
Sacrifice: Hit points you sacrifice for something is damage that you willingly take on yourself. This damage cannot be mitigated or negated by any normal means. If it is, the triggering effect fails. A GM is the final arbiter of how sacrifices are resolved.