Immunity
Source Player Core pg. 400
When you have immunity to a specific type of damage, you ignore all damage of that type. If you have immunity to a specific condition or type of effect, you can't be affected by that condition or any effect of that type. You can still be targeted by an ability that includes an effect or condition you are immune to; you just don't apply that particular effect or condition.
If you have immunity to effects with a certain trait (such as death effects, poison, or disease), you are unaffected by effects with that trait. Often, an effect both has a trait and deals that type of damage (such as an entropy strike spell, which has the void trait and deals void damage). In these cases, the immunity applies to the effect corresponding to the trait, not just the damage. However, some complex effects might have parts that affect you even if you're immune to one of the effect's traits; for instance, a spell that deals both fire and acid damage can still deal acid damage to you even if you're immune to fire.
If you have immunity to effects with a certain trait (such as death effects, poison, or disease), you are unaffected by effects with that trait. Often, an effect both has a trait and deals that type of damage (such as an entropy strike spell, which has the void trait and deals void damage). In these cases, the immunity applies to the effect corresponding to the trait, not just the damage. However, some complex effects might have parts that affect you even if you're immune to one of the effect's traits; for instance, a spell that deals both fire and acid damage can still deal acid damage to you even if you're immune to fire.
Immunity to Critical Hits
Source Player Core pg. 400
Immunity to critical hits works differently. When a creature immune to critical hits is critically hit by a Strike or other attack that deals damage, it takes normal damage instead of double damage. This does not make it immune to any other critical success effects of the actions, such as a critical specialization effect or the extra damage of the deadly trait. However, in some cases the GM might determine the added effects don't apply.
Immunity to Nonlethal
Source Player Core pg. 400
Another exception is immunity to the nonlethal trait. If you're immune to nonlethal, you're immune to all damage from attacks and effects with the nonlethal trait, no matter what other type the damage has. For instance, a typical construct has immunity to nonlethal attacks. No matter how hard you hit it with your fist, you're not going to damage it. You can take a penalty to remove the nonlethal trait from your fist, and some abilities give you unarmed attacks without the nonlethal trait.
Temporary Immunity
Source Player Core pg. 400
Some effects grant you immunity to the same effect for a set amount of time. If an effect grants you temporary immunity, repeated applications of that effect don't affect you for as long as the temporary immunity lasts. Unless the effect says it applies only to a certain creature's ability, it doesn't matter who created the effect. For example, the blindness spell says, “The target is temporarily immune to blindness for 1 minute.”